Index Numbers (Edexcel GCSE Statistics)
Revision Note
Written by: Roger B
Reviewed by: Dan Finlay
Index Numbers
How do I calculate index numbers?
Index numbers are a way of comparing how the prices of items change over time
Prices are compared to what they were in a base year
This is a year chosen to be the 'starting point' for the index numbers
The index number for the base year is 100
The index number is calculated by the formula
Note that this is very similar to calculating a percentage
But percentage signs are not used with index numbers
This formula is not on the exam formula sheet, so you need to remember it
For example, the price of a pint of milk in 2024 is 66p
If we use 2007 as the base year, when the price of a pint of milk was 36p
then the 2024 index number for milk would be
Note that:
An index number greater than 100 means an increase in price
An index number less than 100 means a decrease in price
A base year doesn't have to be at the 'beginning' of a set of index numbers
For example, you could choose 2015 as the base year
And use that to calculate the index number for 2012
What else can I do with index numbers?
Index numbers can be used to find the percentage change in prices between the base year and another year
Subtract 100 from the index number for the other year
The result is the percentage change compared to the base year
A positive result means a percentage increase, a negative result means a percentage decrease
For example the base year for widgets is 2020, and the index numbers for 2022 and 2023 are 112.3 and 98.4 respectively
The percentage change from 2020 to 2022 is (a 12.3% increase)
The percentage change from 2020 to 2023 is (a 1.6% decrease)
Index numbers can be used to calculate a changed price between the base year and another year
Divide the index number for the other year by 100 to find the 'percentage change multiplier' for the change
Multiply the price in the base year by that multiplier to find the price in the other year
Or divide the price in the other year by that multiplier to find the price in the base year
For the widgets example above, the multiplier for 2020 to 2022 is
If a widget cost £14.95 in 2020
then a widget in 2022 cost (round money to the nearest penny!)
The multiplier for 2020 to 2023 is
If a widget cost £14.71 in 2023
then a widget in 2020 cost
What is the retail price index (RPI)?
The retail price index (RPI) is an index number calculated to show the rate of change of prices for things people use in everyday life
It includes such things as food, heating, petrol prices and mortgage payments
The RPI is used by the UK government to set the interest rates paid on student loans
You can use RPI index numbers just like you use other index numbers
For example, if the RPI base year is 1987 and the RPI for 2024 is 378.0
then the 'percentage change multiplier' from 1987 to 2024 is
If a litre of petrol cost 37p per litre in 1987
then an estimate for its price in 2024 would be
This is an estimate because the RPI is calculated based on the prices of lots of different things that people buy
It is not just an index number for petrol
What is the consumer price index (CPI)?
The consumer price index (CPI) is also an index number calculated to show the rate of change of prices for things people use in everyday life
It is similar to the RPI but does not include mortgage payments
The CPI is used by the UK government to determine benefits and state pension payments
You can use CPI index numbers just like you use other index numbers
For example, if the CPI base year is 2015 and the CPI for 2024 is 131.5
then the 'percentage change multiplier' from 2015 to 2024 is
If a basket of shopping costs £80 in 2024
then an estimate for its price in 2015 would be
This is an estimate because the CPI is calculated based on the prices of lots of different things that people buy
It is not just an index number for the items in that basket of shopping
What is gross domestic product (GDP)?
Gross domestic product (GDP) is the total value of all the goods and services produced by a country during a particular time period
Goods are things that are made or produced (food, manufactured items, etc.)
Services are things that people do for other people (e.g. haircuts, bus rides, repair work, medical care)
GDP figures in the UK are usually reported quarterly
If a country's GDP falls (i.e. decreases) for two or more quarters in a row, then the country's economy is said to be in recession
Note that GDP is not an index number
Examiner Tips and Tricks
The index number formula is not on the exam formula sheet, so make sure you remember it
Remember that RPI and CPI are both index numbers and can be used like other index numbers
But they are based on the prices of lots of different items
So you can only estimate the prices of specific items using them
Worked Example
(a) The following table shows the prices of widgets from 2012 to 2015
Year | 2012 | 2013 | 2014 | 2015 |
---|---|---|---|---|
Price of widget (£) | 12.95 | 13.50 | 13.85 | 14.10 |
Index number |
Using 2013 as the base year, calculate the index numbers for the other years and complete the table. Give your answers correct to 1 decimal place.
The index number for the base year is always 100, so that is the index number for 2013
For the other years use
Note that it doesn't matter that 2012 is before the base year 2013!
Year | 2012 | 2013 | 2014 | 2015 |
---|---|---|---|---|
Price of widget (£) | 12.95 | 13.50 | 13.85 | 14.10 |
Index number | 95.9 | 100 | 102.6 | 104.4 |
The base year for calculating index numbers for thingummies is 2012. The index number for 2015 is 97.4 and the index number for 2020 is 107.2.
(b) Find the percentage change in the price of thingummies from 2012 to 2015. Be sure to specify whether it is an increase or a decrease.
Subtract 100 from the index number for 2015 to find the percentage change
That is negative, so it's a decrease
2.6% decrease
In 2012 a thingummy cost £56.50.
(c) Find the cost of a thingummy in 2020.
Divide the 2020 index number by 100 to find the 'percentage change multiplier'
Multiply the 2012 price of a thingummy by this to find the 2020 price
It's money, so round to the nearest penny
£60.57
Weighted Index Numbers
How do I calculate a weighted index number?
For index numbers based on the prices of several different items a weighted index number is used
A different weight is given to each item depending on how important it is
The weight used for each item can change from year to year
Weighted index numbers are calculated using the formula
The weighted index number for the base year is 100
See the 'Other Types of Mean' revision note for how to calculate a weighted mean
This formula is not on the exam formula sheet, so you need to remember it
The only difference from the basic index number formula is that it uses weighted mean prices
The retail price index (RPI) and consumer price index (CPI) are both weighted index numbers
The weights used change from year to year according to changes in consumer spending habits
Worked Example
Roger orders pizza from Lenny and John's Pizzeria as often as he can. He recorded all the pizzas he ordered in 2019 and 2023, along with the price for each variety.
Variety | Price (2019) | Number ordered (2019) | Price (2023) | Number ordered (2023) |
---|---|---|---|---|
Cheese | £13.60 | 12 | £16.20 | 9 |
White | £19.10 | 5 | £22.00 | 7 |
Sicilian | £14.60 | 3 | £17.20 | 8 |
Grandma | £20.00 | 6 | £22.80 | 4 |
(a) Calculate the weighted means for 2019 and 2023.
Use
The weights will be the 'number ordered' for each type of pizza
It's money, so round the 2023 value to the nearest penny
2019 weighted mean = £16.25
2023 weighted mean = £18.88
(b) Work out the weighted index number for Roger's pizzas in 2023, taking 2019 as the base year. Give your answer correct to 1 decimal place.
Use
Round to 1 decimal place
116.2
Chain Base Index Numbers
How do I calculate a chain base index number?
A chain base index number (or chain based index number) is an index number comparing prices in one year with prices in the previous year
There is no fixed 'base year'
Instead each year is compared with the year before
Chain base index numbers are calculated using the formula
This formula is not on the exam formula sheet, so you need to remember it
You can also calculate chain base index numbers to compare prices from month to month
To do this change the formula to
Similarly you can calculate chain base index numbers for other time periods
quarter to quarter, week to week, etc.
What else should I know abut chain base index numbers?
You can find percentage changes and calculate (or estimate) changed prices using chain base index numbers
This works exactly the same as for basic index numbers
Except you only look at changes for one year (or month, etc.) compared to the previous year (or month, etc.)
The previous year (or month, etc.) acts as the 'base year (or month, etc.)'
For example, if the chain base index number for June 2023 is 100.6 compared to May 2023
then the percentage increase from May to June is
And if the price of the item being tracked was £35 in May 2023
then the price in June 2023 would be
The UK government also publishes chain base versions of the retail price index (RPI) and consumer price index (CPI)
Both year to year and month to month versions are published
The year to year versions are used to define the rate of inflation
This is the change in 'average' prices from one year to the next
Usually the CPI is used
but sometimes the RPI is used instead
Figures for the UK gross domestic product (GDP) are published every quarter
Quarter to quarter chain base index numbers are calculated for these
If there is a percentage increase (chain base index number greater than 100), then the economy is growing
If there is a percentage decrease (chain base index number less than 100), then the economy is shrinking
Examiner Tips and Tricks
Read questions carefully to see if a year to year or month to month chain base index number is needed
Worked Example
The table shows the prices for gold sold by a particular dealer for four months in 2020.
Month | April 2020 | May 2020 | June 2020 | July 2020 |
---|---|---|---|---|
Price of gold (£ per gram) | £42.61 | £44.17 | £44.58 | £45.71 |
(a) Calculate the chain base index numbers for April 2020 to May 2020, and for June 2020 to July 2020. Give your answers correct to 1 decimal place.
These are month to month, so use
Round to 1 decimal place
April 2020 to May 2020: 103.7
June 2020 to July 2020: 102.5
The chain base index number for March 2020 to April 2020 is 106.2.
(b) Find the price per gram that the dealer was selling gold for in March 2020.
Divide the chain base index number by 100 to find the 'percentage change multiplier'
March 2020 is the 'base month' for the chain base index number
So divide the April 2020 price by that to find the March 2020 price
This is money so round to the nearest penny
£40.12
Last updated:
You've read 0 of your 10 free revision notes
Unlock more, it's free!
Did this page help you?