Quibans 107: Shrinkflation revisited

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?

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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?

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

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:

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

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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