Wednesday, 9 March 2022

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

 

Sunday, 13 February 2022

Quibans 104: Basket Case

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

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Monday, 22 November 2021

Quibans 103: Over-subscribed

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?

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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? 

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(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 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 ...