Quibans

Quibans 110: American eating habits

noreply@blogger.com (Mr Dawes) — Thu, 31 Oct 2024 00:35:00 +0000

From the Daily Telegraph

My British mind boggles at American eating habits

Outside a convenience store in Kansas, I got talking to a man eating a “Midwest breakfast”: egg and bacon pizza, accompanied by a 36-ounce soda (containing 120g of sugar) and a pint of “americano”.

According to a 2023 study conducted by the Oxford University information platform, Our World in Data, “the average American buys 3,868 calories a day”. But the significant take-away here (pun intended) is that not all the food that gets bought actually gets eaten.

According to Feeding America, a nationwide network of foodbanks, around 38 per cent of the country’s food gets wasted every year. That’s 80 million tonnes, or 145 billion meals, valued at a staggering $444 billion.

Additional information. This could be given to students, or they could be asked to search for it (or could just be told that they don’t have enough information to answer a couple of the questions and will need to work out what additional info they need).

· According to the NHS website, “As a guide: an average man needs 2,500kcal a day, an average woman needs 2,000kcal a day”.

· A sugar cube weighs about 4g, and contains 16 calories.

· The population of the USA is 337 million.

Some possible questions:

1) How many calories are wasted per person per day on average?

2) How many tonnes of food is bought every year?

3) How many meals are eaten per year in the USA? How many is that per person per day?

4) What is the weight of one meal?

5) How much does a meal cost, on average?

6) What percentage of additional calories above the recommended amount are consumed by the average American?

7) What percentage of the daily calories for a man are in the “36-ounce soda”?

Answers:

1) How many calories are wasted per person per day on average?

38% is wasted, so if 3,868 calories are bought per person then we can find 38% of that, which is 1470 calories.

2) How many tonnes of food is bought every year?

80 million tonnes is 38%, so we need to divide by 0.38 to give 210.5 tonnes (more appropriately rounded to 210 tonnes?)

3) How many meals are eaten per year in the USA? How many is that per person per day?

145 billion divided by 0.38 = 381.6 billion. Divide by 365 and then divide by 337 million, to get 3.1 per person per day. This suggests that children are included in the figures.

4) What is the weight of one meal?

80 million tonnes is 80 billion kg. 80 billion kg divided by 145 billion meals gives 0.551724 kg per meal, which is about 550g.

5) How much does a meal cost, on average?

444 billion dollars divided by 145 billion meals = $3.06 on average. [Why is it OK for us to use the figures in the article to work out the answers to Q4 and Q5, rather than needing to find the total cost for all of the food? Both versions work!]

6) What percentage of additional calories above the recommended amount are consumed by the average American?

38% of the calories bought are wasted, so that leaves 2398.16 (call it 2400 calories) being consumed per person. If the population were half men and half women then the recommended daily amount would be 2250 (the average of 2000 and 2500), but the inclusion of children would affect that figure. The average excess is at least 2400 – 2250 = 150. Then divide by 2250, to give 7%.

7) What percentage of the daily calories for a man are in the “36-ounce soda”?

120 g of sugar in the fizzy drink, which is 120/4 = 30 sugar cubes! 16 calories in each cube gives 480 calories. 480/2500 = 19.2%

Sources: https://www.telegraph.co.uk/travel/comment/my-british-mind-boggles-at-american-eating-habits/

https://www.nhs.uk/live-well/healthy-weight/managing-your-weight/understanding-calories/

Quibans 109: Will supermarket sandwich prices really jump?

noreply@blogger.com (Mr Dawes) — Sat, 16 Mar 2024 14:43:00 +0000

From the Daily Telegraph

Supermarket sandwich prices to jump

Sainsbury's and M&S supplier warns bigger wage bill will drive up costs

Supermarket sandwiches are to become more expensive as a looming rise in minimum wage puts up the cost of making them.

Greencore, the UK’s biggest sandwich maker, said on Thursday it would need to increase its prices when the National Living Wage increases by £1 an hour in April.

The company produces 779 million sandwiches a year and supplies most of the major supermarkets, including Sainsbury’s, Marks & Spencer and Co-op.

Greencore chief executive Dalton Philips said: “We’re hugely supportive [of wages rising], because if you can get wages moving again, that’s going to ultimately put more money in people’s pockets. But the reality is, on our wage bill, it is a material increase.”

The National Living Wage will rise to £11.44 from April in the biggest cash increase since the minimum wage was created in 1998. Mr Philips said the increase will add around £30m to Greencore’s costs.

He said: “Obviously you do everything you can to mitigate it by operational efficiencies and all the good work that all companies try. But at the end of the day, it’s £30m, and you can’t mitigate it all. And some of that does seep into price rises.”

Greencore employs around 13,600 people across 16 factories in the UK. As well as making hundreds of millions of sandwiches, it makes around 25 million packs of sushi and 132 million chilled ready meals every year.

Supermarkets ultimately set the price of the goods they sell. However, a rise in what Greencore charges may well be passed on to shoppers.

The likely increase threatens to reverse the recent slide in food inflation. Grocery inflation dropped from 7.7pc to 6.7pc last month, according to the British Retail Consortium.

Industry bosses have warned that they face significant increases in costs in the months ahead that threaten to push up prices. As well as the rise in minimum wage, business rates are also set to climb and new border checks will add to costs.

Helen Dickinson, chief executive of the BRC, said earlier this month: “Government should think twice before imposing new costs on retail businesses that would not only hold back vital investment in local communities, but also push up prices for struggling households.”

Mr Philips said despite the cost-of-living crisis, shoppers were increasingly opting for pricier, premium sandwiches.

This article appeared in the Daily Telegraph in January 2024. I printed the text above out and asked my class to read it. I wanted them to decide what they wanted to explore, and to highlight anything that might be helpful to them.

We then decided we were interested in the following:

1) Is it really an increase in costs of £30 million?
2) How many sandwiches does a worker make each hour?
3) How much will the cost of a sandwich rise by because of the increase in minimum wage?

We deleted the irrelevant information and ended up with this:

Supermarket sandwich prices to jump

Sainsbury's and M&S supplier warns bigger wage bill will drive up costs

The National Living Wage increases by £1 an hour in April and will rise to £11.44. Mr Philips said the increase will add around £30m to Greencore’s costs.

Greencore employs around 13,600 people across 16 factories in the UK. As well as making 779 million sandwiches, it makes around 25 million packs of sushi and 132 million chilled ready meals every year

1) Is it really an increase in costs of £30 million?

The students and I used a number of different assumptions/methods to work this out.

I did this: Assume 37.5 hours per week (max working time), over 48 weeks in the year (not bank holidays, and then some other holiday given too), which gives 1800 hours per employee per year.

Then multiply that by 13,600 employees to give 24,480,000. This is about 24.5 million hours worked per year, so the increase in salaries would be about £24.5 million.

Some students took 9 to 5 as workday and got 40 hours per week. They assumed a 50 week year, and got 2000 hours, giving £27 million.

We talked briefly about on-costs, where employers also pay some national insurance. We decided that the £30 million figure in the article was OK.

2) How many sandwiches does a worker make each hour?

Maybe a “chilled ready meal” is bigger than a sandwich, so perhaps we should count that as being equivalent to 2 sandwiches in terms of making-time? 779m sandwiches + 25 sushi + 132 x 2 ready-meals = 1 billion products. Divide 1 bn by 13600 workers and then by 1800 hours per week to get 40 products per hour.

If you don’t double up for the ready meals you get 936 million meals and the results are similar.

3) How much will the cost of a sandwich rise by because of the increase in minimum wage?

An extra £1 of salary per hour means that each one will need to rise in price by … 100 pence divided by 40 = 2½ pence !

Alternatively, some students divided the increase of £30 million by 936 million to get 3.2 pence.

We have therefore worked out that the price should rise by about 3 pence per sandwich. Given that they cost several quid, that’s about a 1% rise in price. Hardly the ‘jump’ that the headline suggests!

What is the rest of the price of a sandwich made up of? They had ideas like:

The ingredients
Equipment, maintenance, factory cleanliness, safety/hygiene certificates
Staff training (eg hygiene)
Transporting the sandwiches to shops
The shop has to pay its staff, to advertise, to pay rent, to heat/light/clean the shop
Profits (for the sandwich company and the shop)
Etc…

Source: https://www.telegraph.co.uk/business/2024/01/25/minimum-wage-increase-cost-of-supermarket-sandwiches/

Quibans 108: Teacher training crisis

noreply@blogger.com (Mr Dawes) — Fri, 02 Jun 2023 12:53:00 +0000

From The Times Newspaper:

The over-55s keeping classrooms going amid a teaching crisis

Richard Lewis will be 70 on Tuesday. A former City banker, he plans to ride a motorbike until he is 80 — and be a teacher for as long. He is one of a growing number of over-55s propping up classrooms all over England amid a teacher shortage crisis. It is the only age group in which teacher training recruits have increased over the past year.

Despite rising during the pandemic, the number of teachers being recruited has plummeted in the past year. A total of 28,991 teachers were recruited in 2023, down from 36,159 in 2022, according to the Department for Education. Secondary school postgraduate recruitment is 41 per cent below target.

One factor being blamed for the collapse in new trainees coming forward and the high rate of new teachers quitting is what is being called the work-from-home factor. Younger people are shying away from a job in Britain that is still five days a week “in the office”.

Questions:

Q1) Critique the first graph. What is good about it? What is bad about it?

Q2) How many years are included in each of the age bands (apart from the first and last)?

Q3) What is the percentage change from 2021/22 to 2022/23 for each age band?

Q4) What is the percentage change from 2019/20 to 2022/23 for each age band?

Q5) What percentage of the people in 2022/23 are in each age band?

Q6) The headline reads: “The over-55s keeping classrooms going amid a teaching crisis”. Use data/calculations to justify the headline.

Q7) Use data/calculations to help you to write (and justify) a completely different headline.

Q8) What do you think of the headline that was actually used in the newspaper?

Q9) In the second graph, explain what happened in 2021/22. What do the three points mean?

Q10) Tell the ‘story’ of the secondary line in the second graph.

Q11) The article states: “Secondary […] is 41 per cent below target.” Where can this be seen on the graph?

Q12) Why isn’t the ‘total’ dot exactly halfway between the primary one and the secondary one?

Q13) Using 2022/23, work out the ratio of primary trainee teachers to secondary trainee teachers.

A1) Critique the first graph. What is good about it? What is bad about it?

The most unusual/surprising thing is that it goes from right to left! The most recent year is on the left. Does that change students’ perceptions of what is happening?

Is it clear that this shows those who have joined initial teacher training courses, and isn’t the number of new teachers that there are each year?

The age groups are all the same size, except for the first and the last ones. Generally, people start a teacher training course after completing a degree, so it would be rare to be under the age of 21, making the bottom group 21 – 24 rather than 20 – 24. The oldest group covers more than 5 years.

Is the recent year shown in orange to highlight it, or because it is below what it should be?

Would it be useful to have a total at the bottom of each column?

The final ‘bar’ for each year is actually a bar (and not a header/footer). The numbers appear on it for aesthetic reasons.

The bars are useful: they make it easy to see how things are changing (both going up the ages, and across the years).

The years are academic years.

A2) How many years are included in each of the age bands (apart from the first and last)?

“25 – 29 years” consists of 5 years. The way we use ages is that someone is 29 until the day they turn 30. We don’t round off as we usually do. This, then includes everyone who is aged 25, 26, 27, 28 and 29, which is clearly 5 year groups.

A3) What is the percentage change from 2021/22 to 2022/23 for each age band?

(I have put the two columns in the sensible order, unlike in the article!)

A4) What is the percentage change from 2019/20 to 2022/23 for each age band?

A5) What percentage of the people in 2022/23 are in each age band?

A6) The headline reads: “The over-55s keeping classrooms going amid a teaching crisis”. Use data/calculations to justify the headline.

Here’s a possible answer:

“If you look at the percentage change from 2021/22 to 2022/23 (the answer to Q3) you can see that every age group saw a percentage decrease, except one. The percentage decrease was between 15% and 27% (which is more than a quarter). The only group not to see a decrease was the group aged 55 and over, which increased by nearly 4%.”

A7) Use data/calculations to help you to write (and justify) a completely different headline.

There are lots of different possibilities. Here are a couple of ideas:

· Number of new teaching recruits falls by a fifth. (The total from 2021/22 to 2022/23 fell by 19.8%, which is roughly 20%, which is a fifth.)

· The under-25s keeping classrooms going amid a teaching crisis. (Compared to 2019/20, which means they signed up before the pandemic started, the number of new recruits in every age group has fallen. The lowest fall was in the under-25s, which is a good thing, because the vast majority of new teachers are younger than 25. In 2022/23 over 3/5 of the new teachers fell into this group.)

A8) What do you think of the headline that was actually used in the newspaper?

Rubbish!

The number of over-55s training to teach is 160, which is 0.6% of the total. This is a hundredth of the under-25s. The increase from the previous year is indeed 3.9%, but that’s an increase of only 6 people.

A9) In the second graph, explain what happened in 2021/22. What do the three points mean?

The yellow dot for 2021/22 shows that primary recruited ~132% of their target, so they got 32% above the number required.

The light-blue dot for 2021/22 shows that secondary recruited ~78% of their target, so they got 22% below the number required.

The dark-blue dot for 2021/22 shows that overall recruitment (primary and secondary together) was ~96% of their target, which is 4% below the number required.

A10) Tell the ‘story’ of the secondary line in the second graph.

From 2015 onwards it is more or less the same percentage of the target (just over 80%), until 2020/21, which was during the pandemic. Then it increased to just over 100% of target for a year, before dropping back down to the usual level in 2021/22 and massively below that in 2022/23.

(Maybe other jobs weren’t hiring during the pandemic, so more people decided to train to be a teacher.)

A11) The article states: “Secondary […] is 41 per cent below target.” Where can this be seen on the graph?

The light-blue dot for 2022/23 is at 59%, which is 41% below 100%.

A12) Why isn’t the ‘total’ dot exactly halfway between the primary one and the secondary one?

This would only be the case if there were equal numbers of primary and secondary teachers. The total line is always closer to the secondary one, indicating there must be more secondary teachers than primary. (Primary teacher training courses generally cover Early Years (the year before Year 1) and then Years 1 to 6, which is 7 year-groups, while secondary courses generally go from Year 7 to Year 13, which is also 7 year-groups, does this mean that average class sizes in secondary schools are smaller? Or that secondary teachers are more likely to leave teaching so more new teachers are required to replace them? Or … ?)

A13) Using 2022/23, work out the ratio of primary trainee teachers to secondary trainee teachers.

From the graph, the figures appear to be:

Secondary 59%

Primary 94%

Total 72%

If the ratio of primary to secondary is 1 : n, where n is more than 1, we have (94+59n)/(1+n) = 72

Rearrange to get 94 + 59n = 72 + 72n

Solving this gives 22 = 13n, so n = 1.69

The ratio is therefore 1 : 1.69

Source: https://www.thetimes.co.uk/article/the-over-55s-keeping-classrooms-going-amid-a-teaching-crisis-gt3w2269c

Quibans 107: Shrinkflation revisited

noreply@blogger.com (Mr Dawes) — Thu, 27 Oct 2022 22:45:00 +0000

This is taken from a Daily Telegraph article (with paragraphs removed to save space).

Shrinkflation is speeding up at an alarming rate

The Office for National Statistics says food price inflation has risen to 15 per cent. Er, have they been to a supermarket lately? I reckon the cost of basic foodstuffs is up nearer 20 per cent.

And shocking prices are not the only issue. I picked up some dried mango, my daughter’s favourite, to put in the basket yesterday and I thought there must be a hole in the packet because it contained so few pieces. Nope. Same size packaging, half the content. They call it “shrinkflation” – packaging and price stay the same size while contents diminish – and it’s been happening for years. But, if I’m not mistaken, shrinkflation is now speeding up at an alarming rate.

The metric system makes it a lot easier for manufacturers to con consumers – 1lb down to 14oz would be picked up quickly, but 454g to 425g is less noticeable. So, Sensodyne toothpaste is the same price, but tubes are now 75ml instead of 100ml. That’s a 25 per cent price increase. What used to be a 2kg packet of Birds Eye frozen peas has gone down, first to 1.5kg, then 1.3kg and is now a 1.2kg packet.

SEVERAL FOOD ESSENTIALS HAVE SOARED IN PRICE

Price changes between September 2021 and September 2022

Questions

Q1) Is there any contradiction in the first paragraph?

The Office for National Statistics says food price inflation has risen to 15 per cent. Er, have they been to a supermarket lately? I reckon the cost of basic foodstuffs is up nearer 20 per cent.

Q2) What is the percentage change from 1lb to 14oz?

The metric system makes it a lot easier for manufacturers to con consumers – 1lb down to 14oz would be picked up quickly, but 454g to 425g is less noticeable.

Q3) What is the percentage change from 454g to 425g?

Q4) Why has the author chosen 454g?

Q5) Convert 425g to ounces.

Q6) What error has the author made regarding the weights? Correct the sentence.

Q7) What is the error in the toothpaste example? Correct the sentence.

So, Sensodyne toothpaste is the same price, but tubes are now 75ml instead of 100ml. That’s a 25 per cent price increase.

Q8) Calculate the missing figures in the table. Then compare them to the original version, shown below in the answers. Comments?

Q9) Birds Eye frozen peas are mentioned. Here they are, as available at Tesco’s. Which one is the best value?

Answers

A1) Is there any contradiction in the first paragraph?

No. “Food price inflation” could have risen to 15% while the “cost of basic foodstuffs” has increased by more than this, because food price inflation includes more than just the basics.

(And presumably the government’s Office for National Statistics is a more reliable source than Someone Who Goes to a Supermarket.)

A2) What is the percentage change from 1lb to 14oz?

1 lb = 16oz. So the percentage change is 2/16 = 12.5%

A3) What is the percentage change from 454g to 425g?

The percentage change is 29/454 = 6.4%

So it is obvious that the first change would be more noticeable, because it is so much bigger!

Q4) Why has the author chosen 454g?

454g is equivalent to 1 lb.

A5) Convert 425g to ounces.

425/454 x 16 = 14.97797. So it is 15 ounces.

A6) What error has the author made regarding the weights? Correct the sentence.

They have tried to say that the same weight reduction is easier to spot in the Imperial system than in the metric system. Unfortunately, they have gone from 16oz to 14oz in Imperial units and 16oz to 15oz when converted to metric units. Oops!

It could be corrected to be either of these:

* 1lb down to 15oz would be picked up quickly, but 454g to 425g is less noticeable.

* 1lb down to 14oz would be picked up quickly, but 454g to 397g is less noticeable.

A7) What is the error in the toothpaste example? Correct the sentence.

The volume of toothpaste has gone down by 25%, but that is not the same as a 25% increase in price.

To find the equivalent price increase, we need to find out what percentage of the new volume we would need to buy to get the original amount of toothpaste. We would need 1 and 1/3 tubes of 75ml toothpaste to make 100ml. That is the same as a 33 1/3 % increase in price.

It could be corrected to be:

So, Sensodyne toothpaste is the same price, but tubes are now 75ml instead of 100ml. That’s a 33 per cent price increase.

A8) Calculate the missing figures in the table. Then compare them to the original version, below. Comments?

You will not have got exactly the same numbers. Nothing is more than a penny away from what you expect, though, so anything further away than this has an error.

What is going on with the sugar and the rice? Presumably the prices are not exact but have been rounded. How it this possible? They must be average costs across lots of different shops.

A9) Birds Eye frozen peas are mentioned. Here they are, as available at Tesco’s. Which one is the best value?

Working out the cost per kg, or the cost per g is a good way to do this.

Strangely, it’s not the largest packet!

Source: https://www.telegraph.co.uk/columnists/2022/10/26/shocking-prices-shrinking-sizes-does-government-need-stop/

Quibans 106: Which animals could you beat in a fight?

noreply@blogger.com (Mr Dawes) — Thu, 29 Sep 2022 00:08:00 +0000

This is based on a survey carried out by the (usually reputable) polling organisation YouGov. Here is my suggestion of how to use this as a lesson.

The lesson materials (but not the answers) are also available on this PowerPoint

I gave out a questionnaire first:

Fight!

Which of the following animals, if any, do you think you could beat in a fight if you were unarmed?

Rat			Lion
House cat			Gorilla
Medium sized dog			Chimpanzee
Large dog			King Cobra
Kangaroo			Elephant
Eagle			Crocodile
Grizzly bear			Goose
Wolf

Which order do you think people will put them in overall?

(easiest to beat = 1, hardest = 15)

Collect the data as a class. How representative is the sample? Will our data reflect the national data well?

Here is an article from Newsweek (a US news magazine):

A Surprising Number of Americans Think They Could Beat Wild Animals in a Fight

A 2021 YouGov survey had revealed that a surprising number of Americans think they could win an unarmed fight against a variety of wild animals.

Reassuringly, the percentage of Americans confident about winning an unarmed fight goes down, the larger the animal.

Most Americans—72 percent—believe they could beat a rat in a fight, which despite the rodent's large teeth, could perhaps be feasible. However, some foolhardy people still believe they stand a chance against some of the scariest animals in Animal Kingdom, such as the grizzly bear, and the crocodile.

It is a criminal offense to hurt animals. Animal cruelty is a federal crime. The animals mentioned below are generally of no threat to humans unless provoked.

Could You Beat a Bear in a Fight?

Americans are not confident in their abilities to beat a grizzly bear in a fight. Only 6 percent believe that they could win. Grizzly bears can stand at a height of up to 8 feet, and the males can weigh up to 1,700 pounds.

They are faster, stronger, better equipped with both teeth and claws, and they have a much higher level of protection with thick fur, skin, fat layers and thicker stronger bones. So both offensively and defensively we are no match for them.

Could You Beat a Crocodile in a Fight?

A bold 9 percent of Americans think they could take on a crocodile, the biggest reptile in the world. Some can reach 20 feet. Males over 17 feet weigh from about 1,760 pounds to 2,200 pounds. Considering that one of the strongest men in the world, Iranian weightlifter Hossein Rezazadeh, was able to lift only 579 pounds, you can see what you're up against.

Possible questions:

Q1) How does your personal order compare with the national figures for the USA?

Q2) How does the class percentage compare with the USA figures?

(What types of correlation might be useful here?)

Q3) In the Newsweek article, what is unusual about the units that are used?

Q4) Covert the units to metric.

Q5) How do you think people in the UK will compare to those from the US?

Answers:

A1&A2) It may be useful to use Spearman’s Rank Correlation Coefficient for Q1 (to compare the rankings of the animals), and the PMCC for Q2 to compare the percentages. It seems unlikely that the percentages will be close, because in class we have such a small sample size, and it may not be a representative sample because everyone is roughly the same age and lives in roughly the same place.

A3) The article says Grizzly bears are 8 feet tall and weigh 1700 pounds. The units are what we would call “imperial units” and which are used in the USA. They call them “units”, “British units”, or “customary units”.

A4) 1 foot is approx 30cm, so 8 feet is about 2.4m.

1700 pounds (1700 lb) can be converted as follows: There are 14 pounds in a stone and 1 stone is about 6.4kg. Alternatively, use 2.2 lb = 1kg.

The bear is about 120 stone (!), or 770kg.

For the crocodile, 20 feet is about 6 metres, and 2200 lb is approx 1000kg, which is 1 tonne.

Hossein Rezazadeh can lift about 260kg.

Now show the table below from the original YouGov data:

Q6) Which figure was used in the graph?

A6) The 72% was used. (Is it reasonable to lump the ‘don’t knows’ in with ‘I could not beat…’?)

Here is one graph that was tweeted out:

Q7) Comment on the graph and the data.

A7) Comments might include:

About twice as many Brits were asked compared to Americans. The data was collected a month apart. Brits were generally much more cautious! For a rat the difference appears to be about 6%, and for a lion the difference appears to be about 6%. But that means only a small fraction more Americans thought they could beat a rat, but that about four times as many thought they could be a lion.

Here is a final graph about the same original data:

Q8) Comment on this graph

A8) Comments might include: Men are always more confident than women from the same country … except for the lion.

As the headline suggests, for the more dangerous animals, US women are more confident they could win than GB men.

Compare the cat and the rat data with the previous graph. The GB men are the most confident group overall. Does this change the way we might interpret the previous graph?

Final thoughts: We could return to the class data that was collected at the start of the lesson. This Quibans shows the importance of: the sample size, the sample that is used and the way the data is analysed and presented.

https://www.newsweek.com/surprising-americans-beat-wild-animals-fight-experts-1691793

https://yougov.co.uk/topics/society/articles-reports/2021/05/21/which-animals-could-britons-beat-fight

https://docs.cdn.yougov.com/mygotrlqrg/YouGov%20-%20Humans%20vs%20animals%20UK.pdf

https://docs.cdn.yougov.com/07vgk5e81j/YouGov%20-%20Human%20vs%20animal%20fight.pdf

Quibans 105: Ukraine

noreply@blogger.com (Mr Dawes) — Wed, 09 Mar 2022 22:54:00 +0000

Below are excerpts from two Guardian articles. This Quibans records the things my class and I did with the articles.

From The Guardian – 3 March 2022

Ukraine’s refugees: how many are displaced and where will they go?

Domestic civilian flights were cancelled on the first day of the invasion. Since then, people have been heading west into neighbouring countries including Poland, Romania, Moldova and Hungary.

More than half – nearly 548,000 – have fled to Poland which shares a 500km border with Ukraine. A further 133,000 have gone to Hungary, 72,000 to Slovakia, 51,260 to Romania, and nearly 98,000 to non-EU Moldova, Europe’s poorest country. A small number, just over 350, have travelled to Belarus.

From The Guardian – 8 March 2022

Britain should refrain from criticising Ireland’s open-door policy towards Ukrainian refugees, an influential Conservative MP has said, after anonymous briefings claimed it was creating a security risk for the UK.
The Irish government minister Roderic O’Gorman told RTÉ’s Morning Ireland that giving shelter to refugees was “the right thing to do”, revealing that 2,200 Ukrainians had arrived in the country since Russia invaded on 24 February, compared with about 300 in the UK.

Possible questions:

Comment on the countries refugees are going to.
Are the numbers on the map and in the article consistent?
Are the numbers accurate?
Which country is supporting the most refugees? (Why is it not necessarily the ‘obvious’ answer of Poland?)
What percentage of the refugees are in each country?
What is the connection between the circles and the number of refugees?

Answers:

1) Comment on the countries refugees are going to.

Those listed are the countries immediately surrounding Ukraine. This is not a surprise, because flights to/from Ukraine are not currently possible, so to leave Ukraine you need to enter a neighbouring country. Many people will want to return home as soon as possible and won’t want to travel further. Some might have family in those neighbouring countries. Given that they are safe in those countries it would be understandable if people didn’t want to travel further. The number of refugees in Belarus is tiny. But Belarus is supporting Russia in their invasion. Perhaps a bigger surprise is the number in Russia; they are presumably ethnic Russians who were living in Ukraine.

2) Are the numbers on the map and in the article consistent?

Largely, yes. Rounding has mostly been carried out appropriately. The only exception is that Slovakia’s figure from the map has been wrongly stated in the article. Interestingly, almost all of the values have been rounded up. The biggest round-down number is for Belarus!

3) Are the numbers accurate?

I have no idea! How do you accurately count over a million people? The source for the data is the UNHCR (The United Nations High Commission for Refugees) and they presumably have a sensible and consistent methodology that they use in different countries.

The interesting ones are that three of the numbers end in 00, which perhaps suggests they have been given as approximations. One of these is for Russia, which seems to make sense too, given that they are not cooperating with the international community particularly well at the moment ...

4) Which country is supporting the most refugees? (Why is it not necessarily the ‘obvious’ answer of Poland?)

Maybe it would be better to compare the number of refugees to the population of each country?

Here are some calculations that I carried out in Excel:

	No. of refugees	Population	Refugees / population	% of the refugees
Poland	547982	37,846,605	0.014479027	52.42%
Slovakia	79059	5,459,643	0.014480617	7.56%
Hungary	133009	9,660,350	0.013768549	12.72%
Romania	51261	19,237,682	0.002664614	4.90%
Moldova	97827	4,033,963	0.024250842	9.36%
Russia	47800	145,934,460	0.000327544	4.57%
Belarus	374	9,449,321	3.95796E-05	0.04%
Other Europe	88147			8.43%

Ireland	2200	4,937,796	0.000445543	0.21%
United Kingdom	300	67,886,004	4.41917E-06	0.03%

Moldova has the most per population. Slovakia is almost identical to Poland. (We also discussed what the values for Belarus and the UK mean.)

5) What percentage of the refugees are in each country?

See the table above.

6) What is the connection between the circles and the number of refugees?

I copied the graph into GeoGebra and drew line segments to measure the approximate diameter of each circle. When I divided the number of refugees by the area of the circle I got similar answers (roughly 160,000) each time, suggesting that the areas of the circles show the values.

Sources:

https://www.theguardian.com/global-development/2022/mar/03/ukraines-refugees-how-many-are-displaced-and-where-will-they-go

https://www.theguardian.com/world/2022/mar/08/uk-should-not-criticise-irish-policy-on-ukrainian-refugees-says-tory-mp

Quibans 104: Basket Case

noreply@blogger.com (Mr Dawes) — Sun, 13 Feb 2022 15:07:00 +0000

This Quibans comes from a BBC story (widely reported elsewhere too) about the rise in price of a basket of items.

Cost of pasta and tinned tomatoes jumps as shop prices rise

The price of pasta, tinned tomatoes and strawberry jam jumped last year as the cost of supermarket staples rose, new figures for the BBC suggest.

Overall, the price of a basket filled with 15 standard food items rose by £#.## or 8%, in just one year.

Changes in the average cost of the food items at Asda, Morrisons, Sainsbury's and Tesco were tracked by retail research firm Assosia.

Some items fell in price, with carrots and mild cheddar seeing small declines.

The same basket of food made up of items from the cheaper "value" ranges at the supermarkets recorded an overall fall in price, down 45p, or 4%. But within that, items such as pasta and vanilla ice cream saw rises of more than 6%.

Other items the firm tracked in the new research for BBC News included tortilla chips, fish fingers, honey, blueberries, carrots and lemons.

Although official figures suggest that the overall cost of living increased by 5.4% in the year to December, this number - known as the inflation rate - can mask some steep rises seen at the tills, especially on everyday items.

There are many factors that can make it difficult to track how prices are changing for households, such as promotions at supermarkets or a lack of availability of certain products.

Questions

1) Some of the numbers/percentages in the first half of the graphic have been hidden. Work them out.

2) There are two errors in the numbers in the second half of the graphic. Can you spot them without needing to use a calculator?

3) What is odd about the value range potatoes?

4) What percentage of the cost of a standard range basket of goods in 2022 is each of the items?

5) Which of the three products in each range is the most expensive compared to its weight?

6) If the baskets of goods had only consisted of the three products shown here, what would the percentage change in the cost of the basket have been?

7) If (from the standard range) you bought an equal weight of spaghetti and potatoes, what would the percentage increase in price be?

8) The standard range potatoes have increased by 2p and by 2%. You would expect these two numbers to be the same only if the original price was £1. Can you explain why it is still possible here? What is the smallest original price that would mean a 2p increase is also a 2% increase? What the biggest original price that would work?

9) What if we wanted an increase of 20p and an increase of 20% ? What is the smallest price that works?

10) The article mentions some of the items that were used to form the basket of food. What do you think of their decisions?

Answers

Q1) Some of the numbers/percentages in the first half of the graphic have been hidden. Work them out. A1) The original graphic (without the hidden numbers) is below.

Q2) There are two errors in the numbers in the second half of the graphic. Can you spot them without needing to use a calculator? A2) The total basket has gone from £11.24 to £10.80, which looks like a fall of 44p, but the change is given as 45p. If the numbers have been rounded to give £11.24 to the nearest penny, but the original values have been used to work out the 45p difference (which is possible) then that means the researchers are using 5 significant figures in their calculations, which seems unlikely to be appropriate/accurate!

If tomatoes going from 28p to 29p gives a 4% increase, then an increase from 27p to 28p in the cost of pasta seems unlikely to be 6%. (It is actually an increase of 3.7%, compared to the 3.6% for tomatoes.)

Q3) What is odd about the value range potatoes? A3) They cost more than the standard potatoes!

Q4) What percentage of the cost of a standard range basket of goods in 2022 is each of the items? A4) Pasta is 4%, tomatoes are 3% and potatoes are 6%.

Q5) Which of the three products in each range is the most expensive compared to its weight? A5) In 2022, in the standard range, 1kg of pasta costs 144p, 1kg of tomatoes is 112.5p and 1kg of potatoes is 39.2p (pasta is the most expensive). In the value range, 1kg of pasta costs 56p, 1kg of tomatoes is 72.5p and 1kg of potatoes is 36.4p (tomatoes are the most expensive).

Q6) If the baskets of goods had only consisted of the three products shown here, what would the percentage change in the cost of the basket have been? A6) Standard: 18% increase. Value: 6% decrease.

Q7) If (from the standard range) you bought an equal weight of spaghetti and potatoes, what would the percentage increase in price be? A7) I multiplied the pasta figures by 5 to give the same weight as the potatoes. The increase is 30.5%.

Q8) The standard range potatoes have increased by 2p and by 2%. You would expect these two numbers to be the same only if the original price was £1. Can you explain why it is still possible here? What is the smallest original price that would mean a 2p increase is also a 2% increase? What the biggest original price that would work? A8) A 2p increase on 96p is a 2.0833% rise. This is rounded (reasonably) to 2%. If the price goes from 80p to 82p then the percentage increase is exactly 2.5%, so 81p is the smallest price that would see a 2p rise also being a 2% (rounded to the nearest whole number) increase. The biggest price that works is £1.33

Q9) What if we wanted an increase of 20p and an increase of 20% ? What is the smallest price that works? A9) 98p

Q10) The article mentions some of the items that were used to form the basket of food. What do you think of their decisions? A10) I was surprised to see lemons and blueberries were included. I expected to see the basket include the 15 most common items bought (so apples and bananas might be included?) Are tortilla chips really more commonly bought than crisps?

Source: https://www.bbc.co.uk/news/business-60290236

Quibans 103: Over-subscribed

noreply@blogger.com (Mr Dawes) — Mon, 22 Nov 2021 13:03:00 +0000

This Quibans is built around a news article from the Cambridge News headlined: “The top 10 hardest primary schools to enrol your children into in Cambridgeshire”.

Unusually, this Quibans starts with a discussion. The article will appear later.

School A has 30 places and 44 applications.

School B has 25 places and 38 applications.

Which school is harder to get a place at?

School A: 14 pupils were declined.

School B: 13 pupils were declined.

So School A is harder to get a place at.

But:

31.8% of applicants to School A were disappointed.

34.2% of applicants to School B were disappointed.

So School B is harder to get a place at.

We could also work out that for each place at School A there were 1.47 applications and for each place at School B there were 1.52 applications. This means that School B had to disappoint a larger proportion of their applicants.

Which is the most appropriate version to use?

Here is the data from the article, with the schools listed in alphabetical order. Rank them according to each method.

	Applications	Places
Fourfields Community Primary School	93	60
Godmanchester Bridge Academy	38	25
Middlefield Primary Academy	44	30
Park Lane Primary and Nursery School	75	60
Peckover Primary School	76	60
Ridgefield Primary School	50	30
Spinney Primary School	74	30
St Alban’s Primary School	58	30
Trumpington Park Primary	80	60
University of Cambridge Primary School	151	90

Which school is the hardest to get into?

Here is the article:

The top 10 hardest primary schools to enrol your children into in Cambridgeshire

The high number of applications these schools received to the places that were available, made them harder to gain a place.

20 NOV 2021

University of Cambridge Primary School, in Cambridge, had the highest number of first preference applications to the number of spaces it had available for children due to start in September 2021.

Top of Form

The hardest primary schools to gain a place in Cambridgeshire have been revealed.

Primary school preference data from Cambridgeshire County Council shows which schools were the most popular with parents and had more first place applications than spaces available.

In Cambridgeshire, the University of Cambridge Primary School is the hardest school to enrol a child at.

It received 151 first place preferences for children to start in September 2021, while the school only had an intake of 90 spaces available.

Top 10 primary schools that were the hardest to get children into in Cambridgeshire

1. University of Cambridge Primary School, Cambridge
Rated outstanding by Ofsted, the school received 151 first preference applications, while it had 90 spaces available.

2. Spinney Primary School, Cherry Hinton, Cambridge
Also rated outstanding by Ofsted, the school received 74 first preference applications, while it only had 30 places available.

3. Fourfields Community Primary School, Yaxley
Rated good by Ofsted, the primary school received 93 first preference applications, while it had 60 places available.

4. St Alban’s Primary School, Cambridge
Rated outstanding by Ofsted, this primary school received 58 first preference applications from parents, and had only 30 spaces available.

5. Ridgefield Primary School, Cambridge
Rated good by Ofsted, it received 50 first preference applications, and had 30 places available.

6. Trumpington Park Primary, Trumpington, Cambridge
This primary received 80 first preference applications, and could offer 60 places.

7. Peckover Primary School, Wisbech
Rated good by Ofsted, this primary school received 76 first preference applications and had 60 spaces available.

8. Park Lane Primary and Nursery School, Whittlesey
Rated good by Ofsted, the school received 75 first preference applications, and had 60 places available.

9. Middlefield Primary Academy, St Neots
Rated outstanding by Ofsted, the primary school had 44 first preference applications, and had 30 spaces available.

10. Godmanchester Bridge Academy, Godmanchester
Rated good by Ofsted, this school received 38 first preference applications and had 25 places available.

Here is my table:

	Applications	Places	number declined	rank based on number	%age declined	%age accepted	Applicants per place	rank based on %age
University of Cambridge Primary School	151	90	61	1	40.4%	59.6%	1.68	3
Spinney Primary School	74	30	44	2	59.5%	40.5%	2.47	1
Fourfields Community Primary School	93	60	33	3	35.5%	64.5%	1.55	5
St Alban’s Primary School	58	30	28	4	48.3%	51.7%	1.93	2
Ridgefield Primary School	50	30	20	5	40.0%	60.0%	1.67	4
Trumpington Park Primary	80	60	20	6	25.0%	75.0%	1.33	8
Peckover Primary School	76	60	16	7	21.1%	78.9%	1.27	9
Park Lane Primary and Nursery School	75	60	15	8	20.0%	80.0%	1.25	10
Middlefield Primary Academy	44	30	14	9	31.8%	68.2%	1.47	7
Godmanchester Bridge Academy	38	25	13	10	34.2%	65.8%	1.52	6

My favourite column is “applicants per place”. What will happen if you find the reciprocal of the numbers in that column? (1 divided by each of the numbers)

If you decided to use the percentage ranking version, why might Park Lane not actually be number 10 in the county?

(Because other schools that don’t appear in the article might, using the percentage version, be in the top 10.)

Source: https://www.cambridge-news.co.uk/news/top-10-hardest-primary-schools-22203950

Quibans 102: Fly me to the match

noreply@blogger.com (Mr Dawes) — Sat, 16 Oct 2021 17:10:00 +0000

This story comes from the BBC Sport website. It was then picked up by other news outlets. Sky Sports included much of the same material, but the final bullet-point comes from their version of the story.

Man Utd defend decision to fly 100 miles to Leicester for Premier League game

United say they would not normally fly to the game but plans changed due to "circumstances". There were reports of traffic congestion on the M6.

Flying is a significant contributor to global warming and world leaders are meeting later this month in an attempt to avoid a climate catastrophe.

Aviation actually only contributes about 3.5% of the world's global carbon emissions, according to Carbon Brief, but only a very small percentage of the world flies frequently, meaning those who do are disproportionately responsible for these emissions.

Domestic flights are the least energy-efficient way to travel, as shown by the graphic below. France has moved to ban all short-haul domestic flights.

In response to BBC questions around the travel plans, United said they:

§ Have a policy to purchase certified green electricity for all club buildings and facilities.

§ Achieved the Carbon Trust Standard certification for a sixth consecutive year in 2020.

§ Achieved 12 consecutive years of energy and carbon reductions through the Manchester United Energy & Carbon Reduction Programme.

Since the programme's launch in 2008, they have reduced annual carbon emissions by over 2,700 tonnes, a reduction equivalent to emissions produced by 540 homes for a year.

Questions:

1) In the table, what hasn’t been explained?

2) What is the link between the two figures in the table for cars?

3) Why might the figure for a bus be less than for a car, but more than for a coach?

4) Look at the final bullet point. How many km driven by car are equivalent to the emissions produced by a home in a day?

Here are the figures used in the table (taken from a government document):

			Diesel
Activity	Type	Unit	kg CO₂
Cars (by size)	Small car	km	0.14024
	Small car	miles	0.2257
	Medium car	km	0.16877
	Medium car	miles	0.27161
	Large car	km	0.20763
	Large car	miles	0.33415
	Average car	km	0.17152
	Average car	miles	0.27603

Questions:

5) From the graphic in the story, a diesel car uses 171g per km. Where is that figure?

6) What is the conversion factor between km and miles (it’s not exactly 1.6) ?

7) Find the average of the km figures for the small, medium and large cars. Is this the same as the average car? Comment!

Here is more data from the government document:

	kg CO₂
Diesel	0.17152
Petrol	0.18014
Hybrid	0.11346
Battery Electric Vehicle	0.05973

Questions:

8) Comment on the choice to use diesel cars in the graphic.

9) Do hybrid cars use their batteries exactly half the time?

10) In the bus data (not yet shown), there is data about Local bus (not-London), Local London bus, Average local bus. Do you expect the London or the not-London figure to be higher? Will the average figure be halfway between the London and not-London figures, or closer to one of them (which one)?

Here is the bus data:

Type	Unit	kg CO₂
Local bus (not London)	passenger.km	0.11974
Local London bus	passenger.km	0.08163
Average local bus	passenger.km	0.10391
Coach	passenger.km	0.02728

Questions:

11) Were you right?

12) How many days of extra CO2 did each player use?

Answers:

1) These are presumably average figures. Some cars will be more polluting than others because they have a bigger engine or are older, etc. The same will be true for planes. They haven’t explained why they used Diesel cars; I assume there are more petrol cars on the road. They haven’t explained the +121g fully. Does that give an equivalent total CO2 rating for a domestic flight of 254g per km?

2) A car with 1 passenger emits 171g per km. Dividing this by 4 for a car with 4 people in it, which gives 42.75g per person – which has been rounded to 43g here. Does this work? A car with an additional 3 people in it will be heavier and will therefore presumably emit more…

3) I guess: a bus will emit a lot more than a car, but carries a lot more people, so the amount per person is less. A coach stops less often than a bus (wasting fuel while idling), and is more likely to have a higher occupancy.

4) 2700 tonnes is the amount of CO2 produced by 540 homes in a year, so that is 5 tonnes = 5000kg per year. This is 5000kg / 365 per day = 13.7kg = 13700g. Dividing this by 171g, gives us 80km. (I don’t know whether ‘produced by 540 homes’ includes the CO2 the occupants emit in their cars, or whether this is just the CO2 emitted by the building itself, for heating, cooking, food, etc.)

5) It looks like they have used the ‘average car’ figure (which seems fair enough). This is 0.17152. It should be rounded to 172g.

6) Dividing the miles figure by the km one gives 1.609 every time. The next digit is either a 3 or a 4, so this is accurate to 4sf.

7) Working out the average of the small/medium/large, we get 0.172213. The ‘average car’ value given is 0.17152, which is slightly different. Presumably they didn’t work out this average but took into account that there are more medium cars on the road than small cars, etc. The figures given for each size of car are already averages and it is sometimes problematic to take an average of averages.

8) Presumably there are more petrol cars on the road than any other type. Did they choose diesel cars because it made cars look better (and therefore made flying look even worse)? Or did they note that hybrids and electric cars and even better, so it would be fair to use diesel as a kind of average figure?

9) Using half petrol and half electric gives 0.11994, whereas the hybrid figure is 0.11346, so it doesn’t use battery for half the km. (Using diesel and electric doesn’t work either.)

10) I expect not-London to be higher, because rural buses will have fewer passengers on them than city buses and London is a big city. There are many more not-London buses though, so I think the ‘average local bus’ figure will be closer to not-London and won’t be halfway between.

11) Halfway between the not-London and London figures is 0.100685 The average is more than this, so it is closer to not-London.

12) We don't know whether they needed a coach at the other end to take them to their hotel, etc, but if we compare a 100-mile flight with a 100-mile coach journey, we get the following (and the distance by road is likely to be longer than 100-miles because on a plane you can go as the crow flies! And if the traffic was bad then the coach will have presumably used more fuel): 254g per km for the flight, subtract 27g per km for the coach gives an additional 227g per km. Multiply this by 160km (equivalent to 100 miles) to get 36.32kg of CO2. At 13.7kg per home per day, that's an extra 3 days worth of home-carbon to make that flight. (And it's not just the players and subs but the rest of the support staff too).

I wonder whether they will drive or fly home ...

Sources:

https://www.bbc.co.uk/sport/football/58938198

https://www.skysports.com/football/news/12040/12435210/manchester-united-defend-decision-to-fly-to-leicester-for-premier-league-match

https://www.gov.uk/government/publications/greenhouse-gas-reporting-conversion-factors-2019

Quibans 101: Criminals' names

noreply@blogger.com (Mr Dawes) — Sun, 16 May 2021 14:22:00 +0000

With thanks to Cat van Saarloos for the data file, here’s a Quibans from the Daily Mirror.

Police release names most commonly linked with crime - and it's bad news for Davids

Bottom of Form

Choosing a baby's name can be a huge decision and many parents spend time agonising over the choices in front of them.

What you are called can have a lasting impact on your life, but can it effect the chances of you ending up behind bars?

Recent research conducted by casino experts Goodluckmate has shown that some names are more common amongst troublemakers in the UK, with David and Sarah topping the list.

Top 10 lawbreaking male names

1. David - 1,010 criminal charges

2. Daniel - 1,001 criminal charges

3. Michael - 895 criminal charges

4. Paul - 874 criminal charges

5. James - 796 criminal charges

6. John - 742 criminal charges

7. Mark - 742 criminal charges

8. Lee - 701 criminal charges

9. Christopher - 691 criminal charges

10. Andrew - 660 criminal charges

Top 10 lawbreaking female names

1. Sarah - 117 criminal charges

2. Amy - 111 criminal charges

3. Claire - 104 criminal charges

4. Lisa - 103 criminal charges

5. Lauren - 101 criminal charges

6. Kelly - 99 criminal charges

7. Rachel - 98 criminal charges

8. Nicole - 85 criminal charges

9. Michelle - 80 criminal charges

10. Louise - 75 criminal charges

A spokesperson for Goodluckmate said: "Our names play a huge part in our identity, but can they influence who we turn out to be? Are there some names that are more likely to end up on a judge’s docket?

"We wanted to find out if a name can make someone more likely to become a criminal, so we made Freedom of Information requests to police forces around the country, asking for the names of people that were charged with crimes in the last two years, so we could discover the names most likely to commit crimes.

"In total, we received 42,671 names from various police forces around the country, allowing us to work out which names had the most criminal charges attached to them."

Here is a first set of questions:

Question 1) What errors can you see in the article?

Question 2) Comment on this sentence: “We wanted to find out if a name can make someone more likely to become a criminal”

Question 3) Is this a good use of public money?

Question 4) What is the problem with saying “people called David are more likely to break the law”?

Question 5) What other information would it be useful to have?

Question 6) How much more likely are men to commit crimes than women?

And possible answers:

Answer 1) Aside from the maths/stats errors that appear below (and which could also fit here), in this phrase “but can it effect the chances” the word ‘effect’ should be ‘affect’.

Answer 2) This is a correlation vs causation misunderstanding!

Answer 3) A casino company submitted a freedom of information request (FOI) to police forces, asking for this information. The police forces legally have to respond to FOI request, which costs time and money. Is it worth it for a request like this? (Well – it produced a Quibans, but I’m struggling to see any other use!)

Answer 4) If the name David is more common then there are likely to be more law-breakers called David.

Answer 5) A list of how common each name is.

Answer 6) On the top ten lists there are 8112 males and 973 females, suggesting that men are 8.3 times as likely to commit a crime than women.

There is further information on the casino website:

The UK’s most popular names

When we look at the UK’s current most popular names, how do they measure up?

Question 7) Any comments about this?

Answer 7) I was wrong! The names David and Sarah don’t appear on the list of most popular names.

But there is more. Here’s the end of the casino article:

Methodology

We made Freedom of Information requests to police forces around the UK asking for data regarding the first names of those who had been charged with a crime in the 19/20 financial year within their area. Of the constabularies we made requests to, 17 were able to send data, amounting to a total of 42,671 names. We then took the total number of people charged with each name, giving us our results.

When looking at the UK’s most popular names, we took the top five names for baby boys and baby girls in the UK in 2019.

Question 8) What’s the problem with their methodology?

Question 9) What would be a more sensible thing to do instead? What other info do you need?

Answer 8) They are comparing the number of crimes committed by people with each name in 2019-2020 with how many babies that name was given to in 2019. If the frequency of names changes year to year, then this is a daft comparison to make, because there won’t be any babies in the crime figures!

Answer 9) It would be more sensible to use name-frequency data from perhaps 30 years ago.

Cat has provided data from the ONS (Office for National Statistics), showing the popularity of each name for each year ending in a ‘4’. Cat’s spreadsheet is here. The students could analyse this.

Here is the start of the spreadsheet for male names:

And here it is with the 10 names highlighted:

My analysis follows (but there are lots of other ways of doing it).

Taking the average position for male names in the years 1964 (babies born then would be 55 in 2019), 1974 (age 45), 1984 (age 35) and 1994 (age 25), gives the following table. David is second on the list:

Name	Average position
James	7.5
David	7.75
Christopher	8
Michael	8
Andrew	8.5
Mark	15.25
ROBERT	15.25
John	17.75
Paul	18
RICHARD	18
MATTHEW	18.25
Daniel	19.25
STEPHEN	21.5
THOMAS	21.5
JONATHAN	23.5
STEVEN	27
PETER	27.25
NICHOLAS	27.75
SIMON	29.25
ANTHONY	30.25
WILLIAM	30.75
ADAM	31.5
Lee	33

Aside from Lee (position 23), the other nine names (which are shown in lower case in the table) are all in the top 12.

If instead we focus only on 1974 and 1984 we get this list:

David	3
Christopher	3.5
James	4.5
Paul	5
Andrew	5.5
Mark	6
RICHARD	6.5
Michael	7
MATTHEW	8
Daniel	10
John	13.5
Lee	13.5

David appears at the top, and all of the ten names are within the top 12.

Sources:
https://www.mirror.co.uk/news/uk-news/police-release-names-most-commonly-24044516
https://goodluckmate.com/misbehaving-monikers
Spreadsheet: https://drive.google.com/file/d/1KrnBfaLiXf1Fjun6exmPXfRPYV_fzX8x/view

Quibans 100: Something Fishy

noreply@blogger.com (Mr Dawes) — Mon, 28 Dec 2020 18:54:00 +0000

This is not a Quibans about politics (and when I use this with my class I won’t be taking about the politics), but it is about common mathematical/statistical errors that people make.

It is unusual in that it starts with a tweet. I don’t usually create a Quibans based on a ‘random person tweeting’, but because this came from the account of a former MEP who has over 70,000 followers, it seems reasonable to do so.

With my class I will start by showing the following images. Here’s the first tweet:

This image was part of that tweet:

Here’s part of an image from one of the other tweets in the thread:

I will ask the class: What questions do you have for me?

I am anticipating some of the following:

1) Where do the numbers come from?

2) What do they mean?

3) What is he working out?

4) Why is he doing it ‘by hand’?

And here are my responses:

1) This is from the ‘Annex’ to the Brexit Trade Deal that was agreed by the EU and the UK government on 24 December and which is due to be voted on by MPs before the end of 2020. This is a printout of pages 893 and 894.

2) It shows the percentage of each type of fish that is allowed to be caught in different areas of sea by UK and by EU fishing boats.

3) The two orange highlighted columns show the percentage for UK boats in 2021 and in 2026. He is working out the average of these for each page.

4) He has presumably used a calculator to add them up and then to divide by the number of types of fish on the page. Why hasn’t he just copied it into a spreadsheet? The document it is in is a pdf, and the annex is an image, so the text can’t just be copied and pasted! I have retyped those two columns (I think I have done it accurately). They are available on this spreadsheet. (The spreadsheet hasn’t been optimised for printing. Pages 1 to 4 include a screenshot of the original document and my typed version of the relevant columns. The final sheet includes all of the typed data.)

Tasks for the students:

A) For page 1, calculate the total and the mean to check the figures he has worked out here. How many different ways can you work out the mean?

B) Now do the same on page 2. What is going on here? (Find the error!)

C) Go to page 4. If he makes the same mistake on page 4 as he did on page 2, what will his calculations for 2021 be? What is the correct mean?

D) Go to the final sheet. What is the mean for all of the fish for 2021? What is it for 2026?

E) Why is it not reasonable to say there is a 2.32% increase? Using his figures and his methodology, what would be a more sensible value to give for the increase?

F) If UK boats catch 20% of a type of fish in one year and 30% the next, why might they not be landing more fish in the second year? What information is missing here?

G) Why can’t we find the mean of the 2021 figures and the mean of the 2026 figures and then calculate the change? (This is a major issue!)

Some answers:

A) This is a nice opportunity to use Excel in different ways. The calculations for page 1 are correct. (He has sensibly rounded the answers for the mean.) We can use =SUM( : ) to work out the total and can then divide that answer by 24 (there are 24 types of fish stocks on the first page) or can do =AVERAGE( : )

B) On page 2 the total for 2026 is correct. But he has then divided by 27. This should be 28. If you use the ‘average’ command on Excel you get the correct answer and this is the same as dividing by 28. Why has he got this wrong? The second page starts with number 25 and goes up to number 52. He has done 52 – 25 = 27. This seems an obvious thing to do for lots of people. Why is it wrong? How many ways can they explain it?

[If you count them you find there are 28 of them. Or you could consider that on page 1 it goes from 1 to 24, but that is clearly 24 different fish – you don’t do 24 – 1. Or: if you subtract 25 you are getting rid of fish number 25 – we need to remove fish number 24 (and the earlier ones), so it should be 52 – 24.]

C) Page 4 includes fish number 77 to 87. If he subtracts then he will assume there are 10 fish on that page, whereas it should be 11. The total is 383.69. He will divide by 10 to get 38.37% whereas it should be divided by 11 to give 34.88%. (In fact he rounded off to 1dp this time and got 38.4%) Note that you can use SUM and AVERAGE in Excel across the blank cells and cells with text in them – it just ignores them and still gives the correct answers.

D) For 2021 the mean is 33.47% and for 2026 it is 35.93%. These are close to the values he gives (of 33.6% and 35.92%) but not identical. In fact, in the tweet he writes about 2020 and not 2021. I tweeted to ask about this, but didn’t receive a reply.

E) He seems to be saying that because the UK share (according to his calculations) is going from 33.6% to 35.92% then that is an increase of 2.32%. We ought to refer to this a an increase of 2.32 percentage points. From the perspective of the UK fishing industry, the percentage is going from 33.6 up to 35.92. This is an increase of 2.32 over the original value of 33.6. That’s actually an increase for the UK boats of 6.9%.

F) The document talks about the percentage of fish that can be caught by the two fishing fleets. It doesn’t confirm that the total amount is the same each year. If 10 tonnes can be caught one year and 1 tonne the next, then 20% of 10 tonnes is 2 tonnes (2000kg) whereas 30% of 1 tonne is 300kg. (I couldn’t find any figures about the total quotas, so I have no idea whether the amounts are the same each year.)

G) There is a massive issue here, which means all of the information in the original tweet (and everything that has happened so far in the earlier tasks) is just nonsense. We cannot find the average of the percentages in the way the former-MEP did, because they are likely to be percentages of different amounts. Here’s a simplified example. If the UK fleet gets 10% of Fish A and 20% of Fish B, it doesn’t necessarily get 15% of all of the fish. Suppose 100 tonnes of Fish A is landed in total and 1 tonne of Fish B is landed then 10% of A is 10 tonnes and 20% of B is 0.2 tonnes. Altogether the UK boats get 10.2 tonnes out of 101 tonnes, which is 10.1%. Or if the UK fleet has 100% of Fish A and 0% of Fish B then it gets 100/101 = 99% of the fish and not the average of 100% and 0%.

Any time you see averages of averages it is worth asking whether it is fair/reasonable to do this!

Sources: https://twitter.com/MartinDaubney/status/1343147201112010753

https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/948104/EU-UK_Trade_and_Cooperation_Agreement_24.12.2020.pdf

Quibans 99: Bus Gate Fines

noreply@blogger.com (Mr Dawes) — Sun, 29 Nov 2020 12:48:00 +0000

‘Bus Gates’ seem to be the new way to restrict access to certain roads. In the past in Cambridge we had rising bollards that would disappear into the road to allow buses and emergency vehicles to pass through. Bus Gates are ordinary roads, with lots of signs and cameras. A new Bus Gate was installed on what had always previously been a clear section of road. The story below is from the Cambridge News.

Thousands of fines issued to people driving through Mill Road bridge bus gate
Nearly 5,000 fines have been issued to people driving over Mill Road bridge.
From August 28 to October 16, 4,840 fines have been issued to drivers. The number of drivers themselves being issued with fines will be fewer, since one driver can receive several fines.
Since the summer, Cambridgeshire County Council has closed the bridge to all traffic except buses, cyclists, and pedestrians.
Prior to fines being issued, there was a grace period of more than two weeks when 1,630 notices were sent out to warn drivers that they were committing an offence and should they do so again, then they would face a fine.
The fine is £60, but is reduced to £30 if the motorist pays within two weeks.
More than 96 per cent of fines paid were just £30.
This means the council has made an estimated £151,008 from the partial closure of Mill Road bridge.
The council said last year money from fines was used for frontline highways maintenance.

You might like to present this to a class and to ask what is wrong with it. Alternatively, the following questions could lead the students:

Q1) Check every number. Which ones are exact? Which ones have been estimated by the journalist?

Q2) How did they do these estimations?

Q3) Which number is definitely wrong? Explain!

Q4) Produce a better version of that number.

Q5) Compare the number of fines issued to the number of notices sent out during the grace period. What can we conclude?

Some possible answers follow.

A1) “Nearly 5,000 fines” – has been rounded.

“4,840 fines” and “1,630 notices”. Is it suspicious that the number of fines (4,840) and notices (1,630) are both multiples of 10? Maybe they have been rounded off? (For both to end in a zero by chance the probability would be 1/100.) It is possible that they are exact, though.

The numbers for the fines are accurate.

“More than 96 per cent” is an estimate, as is “an estimated £151,008”.

A2) 4,840 rounded to the nearest thousand is 5,000.

96% of the fines were £30. Work out 96% of 4,840 and multiply that by £30. Work out 4% of 4,840 and multiply by £60. Add them together. We get £151,008.

A3) £151,008. You can’t possibly get a number that ends in an ‘8’ by adding integer multiples of 60 and 30.

A4) A better answer/method would be to say: there are about 5,000 fines and almost all were £30, so that makes a total of 5,000 x £30 = £150,000. The total is therefore an estimated £150,000 in fines. I think this is the best estimate to give. If you wanted to go more deeply into this we need to decide what the language means. Can we assume “more than 96%” means it’s up to 96.5%? (suspecting that were to be over 96.5% then it would be written as “nearly 97%?).

If so, then a lower bound would be to take 96.5% of the fines as £30 and the rest as £60.

That gives the newspaper figure as an upper bound (but it would need to be a multiple of £30) and 150,282 as the lower bound (but again – needs to be a multiple of 30). The bounds would therefore be 150,300 and 150,990. If we assume the 4840 has been rounded to the nearest 10 then that broadens those bounds just a little. (To be clear, I don’t think any of this is worth doing: £150,000 is a perfectly sensible estimate here!)

A5) The ‘grace period of more than two weeks’ was presumably there to allow those who use the road regularly to realise that they would be fined and to warn them of that. I would expect lots of warnings during the grace period (because it was a new thing) and fewer fines when it was actually rolled out.

We need to find the rate for both numbers. August 28 to October 16: That’s 4 days in August, 30 days in Sept and 16 days in Oct: a total of 50 days. 4,840 fines divided by 50 days gives an average of 96.8 fines per day. (5000 divided by 50 is perhaps more sensible – giving 100 per day.)

The grace period was “more than two weeks”. If that means 15 days then it is was 108.7 per day, if 16 days then 101.9 per day and if 17 days then 95.9 per day.

All of these values are very close to the 96.8 per day that were actually fined. The number of people being fined each day is the same as the number of people who drove through during the grace period. Does that mean the bus gate just isn’t working? Or that the fines are not a deterrent? Or that the grace period was in August, during the holiday times when the traffic was lower anyway, and that the massive increase in traffic on the roads in Sept means a smaller percentage are bursting through the bus gate?

Source: https://www.cambridge-news.co.uk/news/cambridge-news/thousands-fines-issued-people-driving-19173924

Quibans 98: US Election night 2020

noreply@blogger.com (Mr Dawes) — Sun, 22 Nov 2020 13:01:00 +0000

In this Quibans you may want to copy the images so you can project them one at a time. The questions can then be posed verbally.

In the USA’s presidential election, because of the time differences across the country, the polls close on the east coast earlier than elsewhere and they start counting the votes and releasing the results while voting is still taking place in other states.

I expected the states in New England (the north-east of the US) to support Joe Biden, so I was very surprised in the early hours of the following morning to see, on the election webpage of the Wall Street Journal, this (as a ticker running across the screen):

Q1) What does this mean? And what doesn’t it mean?

A1) It would be usual to think of this as “Trump has 23.1% more than Biden”. But we need to be careful. If Biden has 100,000 votes, does that mean Trump has 123,100 votes? Or does it mean that Trump’s lead divided by the total number of votes cast is 23.1% ? We would usually refer to the latter as a lead of “23.1 percentage points” to avoid confusion.

After my surprise at this huge lead, I clicked on the image of the state of New Hampshire to get further information:

Q2) What is going on? What do you notice? What is strange? What can you work out?

A2) So far, 26 votes have been counted! Just 26. And 16 of those went to Trump, while only 10 were for Biden.

The difference between 61.5% and 38.5% is 23.0% - so there must be some rounding involved.

16/26 = 0.61538…, and 10/26 = 0.384615…, so Trump’s figure has been rounded down and Biden’s rounded up, and when we subtract we get 0.230769…, which rounds to 23.1

An alternative way to get this value is to do 6/26 (where the numerator is the difference between 16 and 10).

It says that 1.0% of the expected total vote has been reported. If it’s exactly 1% then we would expect 2600 votes to be cast in the state of New Hampshire altogether. Using the upper and lower bounds of 1.0% we get:

26/0.0095 = 2736.8 – so the upper bound for the total number of votes is 2736 (mustn’t round up!)

26/0.0105 = 2476.1 – so the lower bound for the total number of votes is 2477 (must round up!)

That seems like a small number!

Here is the current state of play in New Hampshire:

Q3) What is surprising?

Q4) How many percentage points is Biden leading by?

Q5) How many votes are still uncounted?

Q6) Biden won all 4 of the electoral college votes from New Hampshire. Why might that be considered unfair?

A3) They have counted 803,831 votes so far – which is a long way above our upper bound of 2736 ! (And Biden managed to overturn Trump’s 6-vote lead!)

A4) Biden is leading Trump by 59,275 votes. Dividing this by the 803,831 votes counted gives us 0.07374…, which is a lead of 7.37 percentage points.

A5) I am deeply suspicious of the figure for the percentage of votes that have been counted, but if we take it as correct we get that 830,831 is between 98.95% and 99.05%

830,831 / 0.9895 = 812,360 (rounding down)

830,831 / 0.9905 = 811,541 (rounding up)

Hence, there are between 7710 and 8529 still to count.

A6) The way the US Presidential election system works, each state votes and then (for 48 of the 50 states) the electoral college votes for that state all go to the winner of the state. In the election in 2000 the state of Florida was won by a margin of only 500 votes. That gave all of the electoral college votes for Florida (25 of them – because Florida has a greater population than New Hampshire) to George W. Bush and resulted in him winning the election.

In New Hampshire, Biden benefited (he got 53% of the votes but 100% of the electoral college votes), whereas in other states Trump benefited from the system. In the 2016 election Hillary Clinton won more votes than Donald Trump, but ended up with fewer electoral college votes, so Trump was the winner.

Here is the final map from 2020:

Q7) Is there more red or blue?

A7) I think there appears to be more red. But because the very big red states in the north have small populations, the number of electoral votes for the blue states (Biden) significantly exceeds the red states (Trump).

The Wall Street Journal provides this as an alternative version of the map:

Q8) What is going on here?

A8) The map has been scaled to show one square for each electoral college vote. (You may want to flick back and forth between the real map and this one. Montana is a particular casualty!). Now there is more blue.

Source: https://www.wsj.com/election-results-2020/live-coverage.html

Quibans 97: Curious coronavirus cases

noreply@blogger.com (Mr Dawes) — Thu, 22 Oct 2020 00:09:00 +0000

This Quibans uses the first part of an article from the Bristol Post, published on Weds 21 October 2020. I intend to use this a bit at a time, asking questions and revealing the next part of the article after each answer. My answers are at the end.

Part 1:

Bristol University coronavirus cases nearing 1,100 as more staff members test positive
The number of staff members to have tested positive for coronavirus at the University of Bristol has more than doubled in a week, latest figures show.

Question 1) The focus here is on the number of members of staff who have tested positive. What percentage of the 1,100 do you guess are staff and what percentage are students?

Part 2:

A total of 1,050 students have tested positive for covid-19 at the University of Bristol

Q2) Now you have got some additional information, calculate the percentage of the cases that are staff and that are students.

Part 3:

A total of 1,050 students have tested positive for covid-19 at the University of Bristol now, together with 19 members of staff, taking the total of confirmed cases at the university to 1,079 - a daily rise of 67 positive tests.

Q3) Any comments?

Q4) What is the actual percentage of cases that are staff and students?

Part 4:

In recent days, the number of new positive tests among students seems to have slowed down and Tuesday saw the biggest rise in six days (83) as the University hadn't confirmed that many positive tests among its students since last Wednesday, October 14, when 126 cases were confirmed. However, the number of positive tests among staff members now seems to be rising quickly, having more than doubled since last Wednesday when eight coronavirus cases were confirmed among university staff.

Q5) What is the percentage increase for staff over the week?

Q6) If the staff cases continue to increase at the same rate, in which week will the number of staff cases reach 1000?

Q7) Why is this unlikely to happen?

Part 5:

Belowis a graph from the article.

Q8) How does it work?

Q9) Work out the numbers for some of the orange bars and blue dots.

Q10) What criticisms do you have of the graph?

Q11) Why is Oct 19 lower?

Answers:

1) It doesn’t really matter what the class suggest; the reason for doing this is that they will very likely get a percentage for the staff that is vastly too low.

2) Presumably that means 50 staff and 1050 students, so 4.5% are staff and 95.5% are students.

3) The numbers don’t add up! 1050 students plus 19 members of staff equals 1069 and not 1079. And the headline says “nearing 1,100”, which is a rounded version of 1069.

4) 19/1069 gives a staff percentage of 1.8%, with 98.2% of the cases being amongst students. This focus on staff seems less than important!

5) Last week it was 8 and now it’s 19, so the multiplier is 19/8 = 2.375, so the increase is 1.375, which is a 137.5% increase.

6) Keep multiplying the number of staff cases by 2.375

After 1 week: 19 x 2.375 = 45.125 (It might appear that we should round this to 45, but it’s not going to be an exact increase, so I am not particularly bothered about using 45.125)

After 2 weeks: 45.125 x 2.375 = 107.171875

After 3 weeks: 107.171875 x 2.375 = 255

After 4 weeks: 605

After 5 weeks: 1436

We could have done this by using 2.3753, etc.

7) 1000 staff would be a considerable fraction of the staff of the university, whereas 1050 students is tiny compared to the number of students. It seems unlikely that this figure will be reached for staff. The student figure is declining after only a few days, so a sustained increase over 5 weeks seems unlikely.

8) It appears that the scale for the yellow bars is on the left hand side, while the scale for the blue dots is on the right hand side. The horizontal lines work for the left hand scale; you have to look very carefully at the tiny marks next to the numbers on the right hand scale.

The first day has 119 cases (the blue dot) and after that the height of the yellow bar is added to the previous day’s blue dot to get the next blue dot.

Q9) If you go to the graph on the website you can hover over the bars and dots to see the actual numbers.

Q10) Plenty of criticisms!

Why doesn’t the right hand scale start at zero? Starting at 100 doesn’t save very much space!

What happened to Oct 8, 10 and 11 ? Given that the blue dots (for the total number of cases) matches up with the yellow bars that have been added on, does that mean about half of the cases shown for Oct 9 were really from Oct 8? How would the graph look different if Oct 8, 10, 11 were included too?

Q11) It seems odd to have Oct 19 being so much lower and the day after much bigger again. Oct 19 was a Monday. The graph shows when cases were confirmed, so presumably this is 24 or 48 hours after the students were given a covid test. It might be that fewer people were tests on 17 or 18 Oct (because it was a weekend).

Source: https://www.bristolpost.co.uk/news/bristol-news/bristol-university-coronavirus-cases-nearing-4627979

Quibans 96: SATS Papers

noreply@blogger.com (Mr Dawes) — Tue, 28 Jul 2020 18:25:00 +0000

This Quibans shows the power of some Core Maths techniques.

Here is part of the original version of an article in the education newspaper Schoolsweek.

Coronavirus: £2.7m cost of shredding cancelled SATs papers revealed
The government has shredded exam papers for this year’s cancelled SATs and phonics tests – writing off the £2.7m they cost to produce.

Something about this didn’t seem quite right, so I did some Core Maths to it.

First of all: it says there were 9 million ‘test papers’ and then looked at the height of a stack of paper 9 million pages tall. My experience of exam papers is that they are usually more than one sheet.

Here is the background knowledge I already had:

· KS2 papers are taken by almost all Year 6 children in state schools in England (not the UK, just England).

· England (not the UK as a whole) has a population of about 56 million people.

· KS1 papers are taken by almost all Year 2 children in state schools in England.

· The phonics screening test is taken by almost all Year 1 children in state schools in England.

· There are 3 maths tests and 3 English tests at KS2, 2 maths tests and 2 English tests at KS1.

Core Maths-ing it

Here’s what I did with it:

· Life expectancy in England is about 80 years. Let’s assume that there are the same number of people at each age (might be a dodgy assumption). 56 ÷ 8 = 7, so 56 million ÷ 80 = 700,000.

· That would give about 700,000 children in each year group – and I will assume they all take the relevant tests.

· Next assumption is that each test booklet has about 20 pages, which means the equivalent of 10 sheets of A4 paper.

· Now it’s just multiplication and addition!

· The six papers that the Y6 children take (3 in maths and 3 in English) have a total of 60 sheets of paper per pupil. That gives 60 × 700,000 sheets overall.

· The four papers that Y2 children take have a total of 40 sheets per pupil: 40 × 700,000 sheets overall.

· The phonics test might be 2 sheets per pupil: 2 × 700,000 sheets overall.

· This gives a final total of 102 × 700,000 sheets, which I will happily round off to 100 × 700,000 and which gives 70 million sheets of paper. This would have a height of about 7.3 km.

That’s nearly 8 times as much as in the article, which feels like quite a big difference!

Let’s check my assumptions. Are any of them likely to be wildly out?

· Number of children in each year group: If anything there are likely to be slightly more than I estimated/calculated because of population growth.

· I didn’t account of children who didn’t take the test though (perhaps because they are in independent schools), so maybe this balances out the previous point?

· I don’t know how many pages each test has, but the ones from previous years are stapled booklets and they last about an hour each. Surely they can’t only be 2 or 3 sheets of paper each?

So I was fairly happy with my assumptions and with my answer of about 70 million sheets of paper.

From the numbers in the article, it appeared that the author had assumed each of the 9 million papers was a single sheet of paper. That seems like it might be a faulty assumption!

Looking things up

Next I looked up some figures to see how accurate my assumptions were.

This article says 600,000 children took the KS2 SATS last year.

This webpage allows you to download SATS papers (KS1 and KS2) from previous years. Here are the figures for 2019:

KS2

English		Maths
Paper 1	32 pages	Paper 1	20 pages
Paper 2	4 pages	Paper 2	24 pages
Paper 3	12 pages (reading booklet) 20 pages (answer booklet)	Paper 3	24 pages
total	68 pages	total	68 pages

That gives 136 sides of paper, which is 68 sheets (because each piece of paper is double-sided!).

When I checked for 2018, the numbers were almost identical (the only difference was that the English answer booklet was 4 pages longer).

KS1

English		Maths
Paper 1	24 pages	Paper 1	20 pages
Paper 2	12 pages (reading booklet) 12 pages (answer booklet)	Paper 2	22 pages
Total	48 pages	Total	52 pages

That gives 100 sides of paper, which is 50 sheets.

Phonics screening test

It looks like (here) that the answer sheet is filled in by a teacher and that would mean each class only needs one copy of the question paper. That’s a single sheet of paper for each pupil.

Comparing my estimate with the looked-up figures

This table shows my estimated calculations and shows a more accurate version using the figures I looked up:

	My estimate	Using the real figures
KS2 papers	60 sheets per pupil × 700,000 pupils	68 sheets per pupil × 600,000 pupils
KS1 papers	40 sheets per pupil × 700,000 pupils	50 sheets per pupil × 600,000 pupils
Phonics test	2 sheets per pupil × 700,000 pupils	1 sheets per pupil × 600,000 pupils
Total	102 × 700,000 sheets A height of about 7.3 km	119 × 600,000 sheets A height of about 7.4 km

I am happy with that!

Do note, that I have still made some estimates when I used the ‘real figures’.

I have assumed there are the same number of children who take the tests in Y1 and Y2 as in Y6. I also haven’t accounted for the class booklets for the phonics test, and for the teacher instructions for the other tests. (I think they provide teacher booklets in every pack of 10 papers, so this will add a couple of pages per pupil overall).

Finally, Wikipedia says the height of the Eiffel Tower is 300m. So if we divide 7.4 km by 300 metres, we get that the height of the stack of paper would be about 25 times the height of the Eiffel Tower.

Are there better representations of the height?

(Another assumption: the paper doesn’t get compressed by the great pile of paper above it!)

The journalist who wrote the article was kind enough to confirm that they did assume that each test paper was a single sheet and added an extra line to the article.

UPDATE (29 July 2020)

Well this is exciting! Since posting this Quibans the original article has been updated and now links here:

By the power of Core Maths!

Using this with a class

I clearly haven’t used this with a class yet. Here is one way I might use it at the start of next term, stressing the importance of Core Maths techniques in realising when something was mis-stated.

Start by showing the excerpt from the article:

Coronavirus: £2.7m cost of shredding cancelled SATs papers revealed
The government has shredded exam papers for this year’s cancelled SATs and phonics tests – writing off the £2.7m they cost to produce.

Questions: What do you think? Do these numbers seem feasible? How could we tell?

Discussion about this. Is it reasonable that 500 sheets of paper are 5.2 cm thick, are the calculations to get the height of a million sheets correct? (Yes to all of these.)

Are there likely to have been 9 million pieces of paper in the tests (no), are the conversions to metres and Eiffel Towers right (yes).

Next question: There _is_ an error. What is it?

(The only thing it could be is the number of pieces of paper.)

Question: What info do you need to work out how many pieces of paper are involved?

In response to the students’ queries, I might give them some of the info from earlier in this post:

· KS2 papers are taken by almost all Year 6 children in state schools in England (not the UK, just England).

· England (not the UK as a whole) has a population of about 56 million people.

· KS1 papers are taken by almost all Year 2 children in state schools in England.

· The phonics screening test is taken by almost all Year 1 children in state schools in England.

· There are 3 maths tests and 3 English tests at KS2, 2 maths tests and 2 English tests at KS1.

· The Eiffel Tower is 300m tall.

They could then work out estimates for the number of children in each year group (again, as I did above), or I could tell them that about 600,000 children in each of the year-groups took the tests.

They could also estimate the number of pages in each test, perhaps comparing with the GCSE exams (or past papers if they didn’t get to sit the exam), or recalling their own SATS tests.

Or I might give them this information:

KS2

English		Maths
Paper 1	32 pages	Paper 1	20 pages
Paper 2	4 pages	Paper 2	24 pages
Paper 3	12 pages (reading booklet) 20 pages (answer booklet)	Paper 3	24 pages
total	68 pages	total	68 pages

KS1

English		Maths
Paper 1	24 pages	Paper 1	20 pages
Paper 2	12 pages (reading booklet) 12 pages (answer booklet)	Paper 2	22 pages
Total	48 pages	Total	52 pages

Phonics screening test

One sheet of paper for each pupil.

It is worth checking they are clear that they need half as many sheets of paper as there are sides.

They might get calculations that look approximately like mine:

	My estimate	Using the real figures
KS2 papers	60 sheets per pupil × 700,000 pupils	68 sheets per pupil × 600,000 pupils
KS1 papers	40 sheets per pupil × 700,000 pupils	50 sheets per pupil × 600,000 pupils
Phonics test	2 sheets per pupil × 700,000 pupils	1 sheets per pupil × 600,000 pupils
Total	102 × 700,000 sheets A height of about 7.3 km	119 × 600,000 sheets A height of about 7.4 km

7.5 km divided by 300 metres = 25, so the stack of paper would be about 25 times the height of the Eiffel Tower.

Final question: Can they think of better representations of the height?

Source: https://schoolsweek.co.uk/coronavirus-2-7m-cost-of-shredding-cancelled-sats-papers-revealed/

[NB: Some of the article appears in screen-shot form because I wanted to show it before it was updated.]

Quibans 95: The 50p at 50

noreply@blogger.com (Mr Dawes) — Wed, 18 Mar 2020 17:35:00 +0000

From the Guardian.

50p at 50: how Britons' living costs have changed since 1969

The 50p coin entered circulation on 14 October 1969, in the run-up to D-Day on 15 February 1971, when the UK finally abandoned shillings and pence and moved to a decimal currency.

The 50p coin was worth a lot then – indeed, more than any coin in circulation now. In real terms it was worth the equivalent of just over £8. Fifty years on, especially after rampaging inflation in the 1970s, the 50p is a shadow of its former self – it has shrunk in size and weight, but above all in value.

But what do these figures mean in real terms? Inflation since 1969 has been an astonishing ## %, with the fast-rising “cost of living” already a major headache for the government at the end of the 1960s.

What is extraordinary about the wages data from the late 1960s is the huge gap between men and women. The ONS New Earnings Survey for 1970 shows that the average full-time male worker was paid £30 a week, while a female full-time worker earned just £16.30. Annually, that worked out at £ ## for men, which is equal to £24,050 today, but only £ ## for women, equal to £ ## today.

A look through the Guardian’s classified job adverts on the day the 50p was launched gives a snapshot of what real jobs paid. The Open University, which had just been established, was hiring professors at £3,780 a year (equal to £ ## today), lecturers on a range of £ ## to £ ## (£20,153-£47,147), and secretaries on £ ## -£1,068 (£12,506-£ ##).

The Open University is still hiring – and its adverts suggest that real pay for academics has barely edged ahead in 50 years. It currently has an advert for a professor of economics on a range of £67,700-£75,800, while it pays lecturers £33,000 to £49,000. But the secretary job pays lots more in today’s money, with the OU advertising a role at £23,000 to £26,000.

Questions:

Work out the numbers that have been replaced by ## symbols.

What is the real-terms increase of salary for Professors, Lecturers and Secretaries (using the top of the pay scale each time)?

Answers:

Inflation since 1969 has been an astonishing 1,554%

The ONS New Earnings Survey for 1970 shows that the average full-time male worker was paid £30 a week, while a female full-time worker earned just £16.30. Annually, that worked out at £1,560 for men, which is equal to £24,050 today, but only £847.60 for women, equal to £13,068 today.

The Open University, which had just been established, was hiring professors at £3,780 a year (equal to £62,532 today), lecturers on a range of £1,240 to £2,850 (£20,153-£47,147), and secretaries on £756-£1,068 (£12,506-£17,668).

Professors: an increase of 21.2%
Lecturers: increase of 3.9%
Secretaries: increase of 47.2%

Source: https://www.theguardian.com/money/2019/sep/14/50p-britons-living-costs-1969-spending

Quibans 94: Transport in Luxembourg

noreply@blogger.com (Mr Dawes) — Tue, 17 Mar 2020 19:26:00 +0000

This is a pre-coronavirus article about public transport in Luxembourg, from the BBC.

Free transport in Luxembourg, but what's the cost?

It has had months of hype and now finally Luxembourg's free public transport has begun.
With a population of only 614,000, it may be one of Europe's smallest countries and the idea is not unprecedented. But the "free mobility" drive has captured the imagination. Buses, trams and trains are now free to ride on and you don't need a ticket.

"The government wants Luxembourg to become a laboratory for mobility," says Mobility Minister François Bausch, who points to the grand duchy's fast-rising population, with a rise of 40% in 20 years.

Travelling on transport will be free for residents and visitors alike, except for first-class train passengers.

The price of the project will be the €41m (£35m; $44m) in lost ticket fares, but that will be shouldered by the taxpayer. "Of course, just because I call it free transport doesn't mean nobody pays," said Mr Bausch, who is part of Luxembourg's green party,

The total cost of running the service is more than €500m so the government sees the lost fare revenue as relatively small.

It was not exactly pricey before 29 February. A fare cost €2, and double for a day pass. Many workers have their annual travel pass subsidised in Luxembourg, so few people spend much on transport anyway.

Luxembourg spends more of its economic output on transport that most other European countries, with a reported €600 a year per person.

Questions:

What was the population of Luxembourg 20 years ago?
What is the exchange rate of the £ to the € , and the £ to the $ ? How can we use these exchange rates to work out the € to the $ ?
Using the cost of running the service and the population, work out how much it costs per person per year. What is strange about this?
Roughly how many public transport journeys are taken each year? How many per week?

Answers:

614,000 divided by 1.4 = 438571, so the population was about 440,000
£1 = €1.1714 £1 = $1.2571 This means €1.1714 = $1.2571 , so €1 = $1.0732
€500m divided by 614,000 people is €814 each. Later in the article it says that it spends €600 per person per year on transport. (Presumably this includes roads as well. And airports?)
A ‘day pass’ used to cost €4 and brought in €41 million. Presumably most people made two journeys each day (there and back?). That’s about 10 million journeys. Dividing this by 50 (approx. number of weeks in a year) gives 200,000 journeys per week. If we were to assume that this is 100,000 people then only a small fraction of the population ever use public transport!

Source: https://www.bbc.co.uk/news/world-europe-51657085

Quibans 93 – Royal Families

noreply@blogger.com (Mr Dawes) — Mon, 16 Mar 2020 13:41:00 +0000

Quibans 93 – Royal Families

from CNN.

Here's how much Europe's royal families really cost

Question 1:

The UK monarchy is twice as expensive as every other one. What is potentially misleading about this?

Answer 1:

The population of the UK is massively bigger than that of Monaco!

Question 2:

If we work out the cost per person in each country, where do you think the UK would be?

Answer 2:

Here is the next part of the article:

Question 3:

If we combine these two images, what can we work out? (Then work it out!)

Answer 3:

We can work out the population of each country.

Here are my workings (with upper and lower bounds included too, perhaps as a talking point):

Question 4:

What else might we need to consider when working out how expensive a Royal Family is?

Answer 4:

There might be lots of other issues. If palaces are being renovated then that will have a one-off cost. The number of ‘working royals’ might be different in different countries, so there are different numbers of people being ‘paid’. More working royals will require more admin support and staff.

This doesn’t factor in the benefits to a nation of having a monarchy. This might include the tourism that is attracted. In the UK system the Queen is the head of state. If we didn’t have a monarchy then we would need a different person doing that role (such as a president) who would need offices, staff, etc, so some of these costs would still be necessary.

Source: https://edition.cnn.com/2020/03/14/europe/european-royal-families-intl/index.html

Quibans 92: Hoarding toilet paper

noreply@blogger.com (Mr Dawes) — Sat, 14 Mar 2020 17:09:00 +0000

Quibans 92 – Hoarding toilet paper

From the Daily Telegraph, near the start of the coronavirus pandemic:

Why the UK won't run out of toilet roll

13 March 2020
As panic over the coronavirus outbreak continues to spread, empty shelves where toilet roll once would have been has become a common sight in many supermarkets. Consumers have been stockpiling the bathroom staple, sparking fears that supermarkets could soon be caught short. However, there might not be any need to panic.

The UK exported $129m (£103m) of toilet roll in 2019 and exports more than it imports.

“As the world’s 11th-largest exporter of toilet roll, at least if our supply routes shut down, we will be able to keep calm, stop exporting, and carry on,” Dr Rebecca Harding of data firm Coriolis Technologies said.

Ireland accounted for $90.4m or ##% of all UK toilet roll exports in 2019 and is dependent on the UK for 80pc of all toilet roll. Dr Harding said the Irish reliance on the UK for toilet roll is evidence of the importance of borderless trade on the island of Ireland.

Questions:

What is the exchange rate?
What percentage of UK exports of toilet roll go to Ireland?
How much does Ireland spend on toilet roll per year?
The population of Ireland is 4.83 million. How much does each person spend on toilet roll per week?
Four sheets of toilet paper cost about 1p. How many sheets is that per person per day?

Answers:

£1 = $1.2524
70%
90.4 million divided by 0.8 = $113 million
45 cents per week
45 cents is about 36p per week. Divide by 7 to get the cost per day and multiply by 4 to find the number. 20.5 sheets per day.

Source: https://www.telegraph.co.uk/business/2020/03/13/uk-wont-run-toilet-roll/

Quibans 91: SPOTY and the Christmas Number 1

noreply@blogger.com (Mr Dawes) — Sun, 15 Dec 2019 20:27:00 +0000

'SPOTY' is the annual BBC 'Sports Personality of the Year'.

This Quibans takes an article from a year ago. It appears that it is updated each year (and is nonsense every time!). The versionfor 2019 has been done as a video (but includes the same graphics as in 2018).

Here I present the article a section at a time, with a question after each. My thoughts and comments appear together at the end. You may want to give students the address of the webpage and ask them to go through it for themselves.

BBC Sports Personality of the Year: How do you win the main award?

14 December 2018
The BBC Sports Personality of the Year 2018 will be crowned on Sunday but what are the key factors in the make-up of previous winners? From birthplace to facial attributes, we've been analysing the ideal candidate...
The award was first handed out in 1954 and there have been 60 different winners, with Andy Murray the only person to win it on three occasions.

Question 1: This image appears at the end of the article. It suggests that to win SPOTY you ideally need to do athletics, to have been born in London, to have blue eyes, to be 29 years old and to have had your achievement in August. Any comments at this stage?

Here is the first image:

Q2) Why might it not be surprising that there are more Athletics winners than there are from other sports?

=============================================

Q3) Why is this unsurprising?

=============================================

Q4) Any comments?

=============================================

Recall the line of text near the start of the article:

The award was first handed out in 1954 and there have been 60 different winners, with Andy Murray the only person to win it on three occasions.

Q6) Looking at the previous image, what can we work out?

=============================================

Q7) Why is this not a surprise?

Q8) So let’s look back at the diagram we started with. Any further comments?

Here are my answers:

Q2) There are lots more athletes than there are motor racing drivers and there are lots of sports included under the heading ‘Athletics’. There are really only 11 England cricketers who might be in with a chance and footballers suffer because people will only vote for national team players and not those from clubs they don’t support,

Q3) London is bigger than anywhere else, so it has a larger proportion of the population.

Q4) What has this got to do with success in sport or with popularity? Does having green eyes make you less popular? No. Does it make you less successful? No. And the facial hair is presumably partly to do with fashion.

Q5) If you have blonde hair you are more likely to have blue eyes! So these two things are linked.

Q6) There are 65 winners here, so some people have won it twice.

Q7) Many awards will have been because of events that take place in the summer, such as the Olympic Games (July/August) or Wimbledon (June). There are most winners from athletics and that is overwhelmingly a summer sport. Is it also likely that those who win things in Jan/Feb/March are forgotten by the time you get to December and the voting for SPOTY?

Q8) We have said already that athletics and August are likely to be linked and that London is the biggest city in the UK, so is likely to have more people who are born there. The blue eye colour is interesting: for the men it was equal, but by including the female winners you get blue being the mode. Clearly, if you are male then this isn’t relevant! But hold on: vastly more men have won than women, so should that be mentioned here?

Here is a list of the Athletics winners of SPOTY (from Wikipedia):

Of the Athletes, 5 were born in London (Christopher Chataway, Seb Coe, Daley Thompson, Fatima Whitbread and Jonathan Edwards).

The final four of those appear to have brown eyes, leaving only Christopher Chataway. He was 23 years old when he won and his big achievement (breaking the 5000m world record) took place in October.

Chataway meets only the first 3 of the 5 criteria. Are there any who meet 4 of them? Jonathan Edwards is the only one of the athletes who makes 4 out of 5. He was a Triple-Jumper, born in London, was 29 and his world championships win was in August.

None of the other winners (from any sport) get 4 of the 5.

So this is an example of where appealing to the averages at every stage doesn’t help us in predicting the winner.

Extension: Number 1 song at Christmas

This used to be one of the biggest songs of the year. Many different newspapers carried exactly the same story. This version comes from the Independent:

Music experts find formula for ‘perfect’ Christmas number one

Music researchers have crunched the numbers on Christmas songs to find the perfect formula for a festive hit.

Experts at a UK music label looked at every Christmas number one from the last 50 years to see what they have in common and determined that the Pet Shop Boys’ 'Always On My Mind' came closest to being the quintessential tune for the holidays.

“I think we’re a long way from an algorithmically-generated Christmas number one,” said Howard Murphy, founder of Ostereo which conducted the research, in a press release accompanying the data.

“But certain characteristics do make a song more likely to resonate with audiences at Christmas,” he added.

For a song to hit the top spot on Christmas Day it needs to be three minutes and 57 seconds, in the key of G major, played at 114 beats-per-minute and performed by a 27-year-old solo artist, according to the research.

Other key trends among the songs analysed were that the majority were ballads, nearly half were cover versions and nearly all were about something other than Christmas.

'Always On My Mind' hits the ideal length and key exactly, as well as being a cover of Elvis’ 1972 hit, but is slightly faster than the formula suggests at 125 bpm and performed by a duo who had an average age of 31.5 when the song hit number one at Christmas 1988.

'Mary’s Boy' by Boney M came a close second, researchers said, with a tempo of 113 bpm, length of four minutes two seconds and a key of F, two semitones lower than G.

Clearly this isn’t a ‘formula’ – they have just averaged the attributes of all the Christmas number one songs over the years. What types of average have they used for each attribute? How is this story related to the SPOTY one?

Sources:

https://www.bbc.co.uk/sport/sports-personality/42367914

https://www.bbc.co.uk/sport/av/sports-personality/50752816

https://en.wikipedia.org/wiki/BBC_Sports_Personality_of_the_Year_Award

https://www.indy100.com/article/christmas-number-one-how-to-guide-perfect-formula-pet-shop-boys-boney-m-elvis-8674946

Quibans 90: Goal sizes

noreply@blogger.com (Mr Dawes) — Fri, 12 Jul 2019 15:19:00 +0000

This task was test-driven at the recent AMSP Core Maths days (as part of ‘Quibans Live’). Thanks to those who made suggestions for improvements.

The story appeared in a number of places before the 2019 FIFA Women’s World Cup and there were discussions about whether women should play with smaller goals because women are, on average, shorter than men. This version is taken from the Daily Telegraph.

'Reducing size of women's goals would not help fight for equality,' says England goalkeeper Karen Bardsley

England goalkeeper Karen Bardsley believes reducing the size of goals in the women's game would jeopardise the fight for equality in football.

Chelsea manager Emma Hayes has suggested the women’s game could be adapted to bridge the ‘physical differences’ between women and their male counterparts.

She suggested smaller goals could stem criticism often directed at female goalkeepers, who are generally of a smaller stature to their male counterparts.

Manchester City goalkeeper Bardsley, about to play in her third World Cup when she will add to her 77 international caps, does not believe narrowing the width between two posts is the way forward.

“My big thing is we need to change how people feel about goalkeeping, I don’t think there is enough respect for the position in the game, whether male or female.

“There is a stigma, that you have to be a certain size, or not very good with your feet, or you have had to go in goal as a last resort.”

How could we explore, using some Core Maths knowledge, whether the goals should be made smaller?

On one level it doesn’t matter. Football is a relatively low-scoring game (compare it with American Football, basketball, rugby, cricket, etc, where the numbers of points (etc) are very much bigger). If the goals are bigger than necessary and this results in more goals being scored then this isn’t a big deal. The goals are the same size for both teams after all.

We could find data for the heights of male and of female goalkeepers and compare them.

In fact, I think the size of the goal was set in the 1866 version of the laws of the game and according to the BBC the “average height of men has risen by almost 11cm since the mid-19th century”.

Wikipedia has the current average height of UK men at 175cm and women at 162cm, so if both have increased by about 11cm since the size of the goals was fixed then women are now roughly the same height as men were back then.

Here’s my favourite way to explore this issue: If the goalposts are too big for women then that presumably means more goals are being scored by women. Let’s use the number of goals per game from the last two World Cups (Russia 2018 for men and France 2019 for women) and compare the data.

The Google Sheets file has the full data, but here are the relevant parts. You might want to give the summary data to the class and ask them to work out averages and interpret them.

Before giving it out you might want to ask whether the average number of goals per game will be different in the group stage or the knock-out part of the tournament.

Is this a reasonable set of calculations to do? Are there ways to improve this?

Those who followed the women’s competition will know that the eventual winners, the USA, beat Thailand 13-0. This is clearly an outlier, so perhaps we should remove it from the women’s data?

At Quibans Live several people pointed out that if there was extra time in a match then there was more opportunity to score goals (the penalties that follow extra time have not been included here, though that is another avenue that could be explored). A normal-length match is 90 mins, so extra-time of 30 mins is equivalent to another third of a match.

Here are the results with the 5 extra-time men’s matches and the three extra-time women’s matches included:

Very close indeed! This data doesn’t suggest the goals should be smaller in the women’s game.

Final thought:

This is clearly relevant to the elite athletes at the last two world cups. Does it still work for those playing at lower levels?

Sources: https://www.telegraph.co.uk/football/2019/05/29/reducing-size-womens-goals-would-not-help-fight-equality-says/

https://en.wikipedia.org/wiki/Laws_of_the_Game_(association_football)#1863_rules

https://www.bbc.co.uk/news/health-23896855

https://en.wikipedia.org/wiki/List_of_average_human_height_worldwide

https://docs.google.com/spreadsheets/d/1PupE-_c8zGfNsRBROBa8urFv48HQqk8oz42qu_lczUc/edit?usp=sharing

Quibans 89 – Men vs Women in the European elections 2019

noreply@blogger.com (Mr Dawes) — Fri, 17 May 2019 19:48:00 +0000

I voted by post earlier in the week. Some parties had more female candidates than others. I wondered whether it was the case that across the country certain types of party have more male or female candidates. Here’s what I did with my Year 12 Core Maths class.

Some background to the electoral system:

Each country in the EU has its own voting system for the European elections. England is divided into 9 regions and Wales and Scotland are each a region (Northern Ireland has a different system, so I didn’t involve them). In each region there are a number of seats, ranging from 10 seat for the South East region to 3 seats in the North East.

You don’t vote for an individual but for a party. Each party has a ‘list’ of candidates for each region. Last time around in the 7-seat East of England region most parties had seven candidates. Having worked out that UKIP should get 3 seats, the Conservatives 3 seats and Labour 1 seat (using the D’Hondt method – but that’s not relevant here), the top three candidates from the UKIP list were elected as MEPs, the top three from the Conservative list and top Labour candidate.

What we did:

On a shared Excel file, I had each region on a separate sheet. I divided these up around the class (some students had a sheet each, others worked as a pair). First they sorted out whether each candidate was male or female. This wasn’t always obvious, so they Googled if they weren’t sure.

Then they typed into another sheet the number of female and male candidates for each party.

They had to deal with some issues. For example, some candidates are standing as ‘independents’, meaning they are not part of a party. We decided to ignore them. Some candidates have withdrawn from the election; we removed the ones we knew about.

These are the results, for the parties that are standing in every region:

11% of the UKIP candidates are female, through to Change UK, for whom 57% of the candidates are female.

Is it interesting that the more pro-Brexit parties tend to have more male candidates, while the more pro-Remain parties have roughly equal numbers of men and women?

Better methodology?

But hold on: maybe this doesn’t tell the whole story. What if the LibDems have the same number of male and female candidates but the top few in each region are all men? It is extremely unlikely that those further down each list will be elected, so this is important.

Here is how I intend to deal with that.

The students recorded a list of Male and Female candidates for each party. Here’s part of that list:

Since the lesson (we will talk about this next week) I have turned that into a set of binary numbers, where F becomes 1 and M becomes 0.

I then turned the binary into a decimal. This means the first-ranked candidate in each list is worth double the one that follows, which is worth double the one after that, etc. If there are 5 candidates in a list, the 5th one is worth 1 point, the 4th is worth 2 points, the 3rd gets 4 points, the second gets 8 points and the first is 16 points. Add up the number of points for the female candidates and then divide by the total (which is 1 + 2 + 4 + 8 + 16 = 31). That gives a fractional weighted-score for the female candidates in each region.

Then I found the average of these.

The second column shows this new figure (with the first column showing the previous data):

Not much difference (apart from the Green Party)!

Final thoughts:

It was good for the students to see a way to carry out this sort of analysis.

It was good to divide up the work. I couldn't find an easy way of getting hold of the gender of each candidate, so sharing the workload was a good thing.

We had to decide how to deal with problems (withdrawn candidates).

We had to think about how to do the analysis.

Here are links to my original spreadsheet and the one my class filled in.

If you want your class to use the original version then you will need to save it and share it with them (your IT people in College will be able to help if you haven't done this before).

Source: https://inews.co.uk/news/politics/european-elections-2019-candidates-mep-who-standing-eu-vote-full-list/

Quibans 88: Bottled water

noreply@blogger.com (Mr Dawes) — Sat, 04 May 2019 16:31:00 +0000

I started by giving out just this paragraph from the Guardian article that follows:

Imagine laying out half-litre bottles on the pitch at Wembley Stadium. You could fit ### bottles on the grass, packed into a tight grid. Now imagine building up layers of bottles, covering the same area, to build a tower. To contain all the bottled water we buy each year [in the UK], you would end up with a ###-metre skyscraper.

There are some nice Fermi estimations required here.

What are the dimensions of a football pitch? What are the dimensions of a water bottle? How many bottles are used in this country in a year?

Then we need to convert some units and carry out the calculations, not forgetting to round off sensibly.

The students worked in groups. A typical estimate for the size of a football pitch was 110m by 60m. Some measured their water bottles (!) and found a diameter of about 6cm and a height of 20cm.

If working out the area covered by the pitch and by a bottle we need to be careful when converting units (10,000 cm² = 1m²). We also need to decide what “packed into a tight grid means” (we took it to mean a rectangular grid). The easiest way is to work out how many bottles fit along each side of the pitch and then to multiply these. These figures gave us 1.8 million (pleasingly close to the 1.7 million in the article). Other estimates in the room varied between 1.6 million and 2.8 million.

Working out the height is more difficult. If everyone in the country has one bottle per week then that would give us about 1.7 billion bottles per year. That would need to be stacked 1000 rows high, which means a height of about 200m. In fact the article says it’s 2.2 billion _litres_ per year (each bottle holds 500ml), so we have underestimated the answer.

I then gave out a fuller version of the article (below) and asked what things they could work out.

If we care about plastic waste, why won’t we stop drinking bottled water?

Sun 28 Apr 2019

For all the innovation and choice that define the food and drink industries, if you want to make money, you could do a lot worse than bung some water in a bottle and flog it. A litre of tap water, the stuff we have ingeniously piped into our homes, costs less than half a penny. A litre of bottled water can cost well over a pound, especially for something fancy that has been sucked through a mountain.

Yet the bottled water market is more buoyant than ever, defying the plastics backlash inspired by stricken albatrosses on the BBC’s Blue Planet, and a broader, growing sense that something has to change.

Sales in the UK were worth a record £558.4m in the year to last November, an increase of 7%, according to the latest figures from the market analyst Kantar. Separate data from the analysts Nielsen show that last year we guzzled more than 2.2bn litres of bottled water, including “take-home” and “on-the-go” products. That’s an annual rise in volume of 8.5%.

Imagine laying out half-litre bottles on the pitch at Wembley Stadium. You could fit 1.7m bottles on the grass, packed into a tight grid. Now imagine building up layers of bottles, covering the same area, to build a tower. To contain all the bottled water we buy each year, you would end up with a 514-metre skyscraper – 200 metres taller than the Shard.
Hope is not entirely out of reach. That plastic skyscraper conceals attempts in the bottled water industry to change. If nothing else, the rate of growth has begun to ease (sales were up 7% in the year to November 2018, compared with 8% the previous year).

But even if large numbers of us are quitting bottled water because of care for the environment, others are taking it up. The introduction of the “sugar tax” on juices and fizzy drinks has pushed more people to bottled water, while health awareness has boosted its desirability. Kantar says tap water consumption is growing at roughly the same pace (we still drink almost three times as much tap water as bottled water).

So the plastic tide only creeps higher. The industry is quick to point out that all its bottles are recyclable. “But collection rates are, at the most generous estimates, 56%, so the actual recycling rate will be lower than that,” Chetan-Walsh says. And while bottles may be recyclable, very few are made of recycled plastic. Highland Spring launched recycled half-litre “eco” bottles alongside its standard bottles in January; Evian has vowed to use only recycled plastic across its range by 2025.

Kinvara Carey, general manager of the Natural Hydration Council, an association of the biggest bottled water manufacturers, cites a survey in which people were asked what they would do if bottled water were not available. “Forty-four per cent would buy another drink, which is not great, 14% would go without and 4.5% said they would find a fountain,” she says. “The choice is important.”

We can work out things like:

1) The cost of a litre of bottled water
2) How the price has changed in the past year
3) What the amounts were last year
4) How many bottles are recycled
5) The volume of landfill taken up by bottles
6) Why the percentages in the final paragraph don’t add up to 100%
7) How much water each person drinks each day

Source: https://www.theguardian.com/environment/2019/apr/28/if-we-care-about-plastic-waste-why-wont-we-stop-drinking-bottled-water

Quibans 87: McDonald’s straws

noreply@blogger.com (Mr Dawes) — Fri, 26 Apr 2019 17:04:00 +0000

I gave the article below (from the BBC website) to my Yr 12 class and asked them what they could work out. They had some great ideas (which are shown below the article), largely because we have been working on this sort of thing throughout the year. If you wanted to use this with a class that isn’t used to working in this way then the ideas my class came up with could be turned into questions to ask.

McDonald's plastic straw petition: Call to ditch paper straws
24 April 2019

McDonald's is being called on to stop its roll out of paper straws in the UK and Ireland, amid claims that they "dissolve" in drinks.

The fast food giant is switching from plastic to paper straws at their 1,361 restaurants after customer pressure. An online petition calling for a return to plastic straws has so far garnered more than 35,000 signatures.

McDonald's say they are "doing the right thing" while a supplier said customers need to "compromise". The restaurant chain supplies 1.8 million straws to its four million UK customers each day.

Things my class worked out:

35,000 people have signed the petition. That’s less than 1% of the people who visit McDonald’s in one day.
About 6% of the population of the country go to McDonald’s each day.
On average each restaurant uses 1323 straws per day. [We talked about rounding this off more appropriately – and decided that 1300 is probably better.]
Just under half (45%) of customers use a straw. This might be because some people don’t have a drink, or have a hot drink, or have juice without a straw.
There are 1.46 billion visits to McDonald’s in the UK and Ireland each year. [Better as 1.5 billion?] We know this can’t be 1.5 billion different people because that would be about a fifth of the population of the planet! On average, that’s 22 visits per year per person, which is equivalent to about two visits per month. Maybe half the population go once a week and the other half never go?
A straw weighs about 0.42g. That means 756kg of straws per day. Over the course of a year that’s the weight of 3600 adults.

Source: https://www.bbc.co.uk/news/uk-wales-48038130

Quibans 86: Recycling Ferrero Rocher

noreply@blogger.com (Mr Dawes) — Sat, 15 Dec 2018 21:16:00 +0000

This is interesting because it contains an error, a lack of clarity and something misleading. Perfect for a Quibans!

Article from the Daily Telegraph:

Ferrero Rocher shamed as Christmas chocolates with the least recyclable packaging

12 DECEMBER 2018

Ferrero Rocher has been named and shamed as the Christmas chocolate box with the least recyclable packaging.

The vast majority (89 per cent) of the packaging in a 359g Ferrero Rocher Collection box may be destined for landfill as it is made from non-recyclable plastic and foil, a study by consumer group Which? found.

By contrast the most recyclable chocolate boxes were Waitrose Christmas Chocolate Favourites 240g which is 96.3 per cent recyclable) Cadbury's Milk Tray, which is 92.5 per cent easily recyclable. The second least recyclable packaging was for Marks & Spencer's The Big One Selection 600g, which is 71.4 per cent recyclable.

In addition Which? analysed chocolate boxes for their packaging to chocolate weight ratio, and found boxes of Ferrero Rocher Collections had by far the highest.

Nearly half of the weight of a 359g Ferrero Rocher Collection box is made up of packaging (42.4 per cent), with the rest constituting (67.6 per cent) the chocolates themselves, it found.

The boxes with the highest proportion of chocolate weight were Marks & Spencer's The Big One Selection 600g (just 8.5 per cent packaging), and Lindt Lindor Assorted Mix 384g (just 11.5 per cent packaging), the study showed.

Questions:

1) What is the error?

2) The lack of clarity is that ‘359g’ is the weight of the chocolate (and nuts, etc) in the box. The packaging weighs more on top of that. 42.4% of the total is the packaging, so what is the weight of packaging?

3) The misleading part is that an implication of the two mentions of M&S is not followed up. What is going on there?

(Answers are below.)

Further info:

Here are screenshots of the tables from the Which? report:

Here it is as a single table (to be pasted into Excel?)

Chocolate	Official weight (g)	Weight in packaging (g)	Packaging weight (g)	Percentage packaging	Percentage easily recyclable
Cadbury's Heroes	660	808	144	17.80%	88.90%
Cadbury's Milk Tray	360	470	106	22.60%	92.50%
Cadbury's Roses	660	810	144	17.80%	90.30%
Chocolate Treats By Sainsburys	650	806	154	19.10%	88.30%
Ferrero Rocher Collection	359	642	272	42.40%	11%
Lindt Lindor Assorted Mix	337	384	44	11.50%	90.90%
Marks & Spencer The Big One Selection	600	662	56	8.50%	71.40%
Mars Celebrations	650	812	150	18.50%	90.70%
Mars Malteaser Teasers	275	364	70	19.20%	88.60%
Morrisons Mega Mix	1050	1216	162	13.30%	81.50%
Nestle Quality Street	720	846	130	15.40%	83.10%
Thorntons Continental Selection	284	408	120	29.40%	86.70%
Waitrose Christmas Chocolate Favourites	240	356	108	30.30%	96.30%

Additional questions:

4) What should happen when you add up the Official Weight and the Packaging Weight columns?
5) Do any of them mis-state the amount of chocolate they contain?
6) Work out the percentage of the Total Weight for each product that cannot be recycled. How does M&S compare?

Answers:

1) The error is that 42.4% plus 67.6% doesn’t equal 100% (and it should). The former figure is correct (as seen in the Which? tables).

2) The chocolate in the Rochers are 57.6%, so when we divide 359g by 0.576 we get the total weight (623g) and this leads to a packaging weight of 264g. This doesn’t agree with the figures from Which? because there is slightly over 359g of choc.

3) M&S may have the second-least recyclable packaging, but there is much less of it, so maybe they have cut down on the packaging overall (which seems like a good thing: just because something is ‘recyclable’ doesn’t mean everyone will recycle it!).

4) You should get the ‘Weight in packaging’ column.

5) Most of them give us slightly more chocolate than advertised, with only Nestle falling under (but that is presumably only on the single box that Which? tested).

6) I used Excel to work this out. 38% of the weight of the in-package Ferrero Rocher is non-recyclable, but only 2% of the M&S. The median was 2%.

Sources:
https://www.telegraph.co.uk/news/2018/12/12/ferrero-rocher-shamed-christmas-chocolates-least-recyclable/
https://www.which.co.uk/news/2018/12/the-truth-about-christmas-chocolate-packaging/