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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