Index Numbers
An index number expresses the value of a quantity, such as price or cost, as a percentage of its value in a chosen base year, which is always given the index value 100. Index numbers make it easy to compare how a quantity has changed over time or between different places, since the percentage change from the base year can be read directly from the index.
Before you start
No specific prerequisites - this is a good place to start.
Method
- Choose a base year or base period and give it an index number of 100.
- Divide the value in any other year by the value in the base year, then multiply by 100 to find its index number.
- Use the formula: index number = (value in given year / value in base year) x 100.
- Interpret an index number above 100 as an increase since the base year, and below 100 as a decrease.
- Find the percentage change from the base year by subtracting 100 from the index number.
- To compare two non-base years, divide their values (or index numbers) and multiply by 100, rather than assuming the base year is one of them.
Worked example
The price of a bus ticket was 1.60 pounds in 2015 (the base year) and 2.00 pounds in 2023. Find the index number for the price in 2023, and state the percentage increase since 2015.
- The base year value (2015) is 1.60 pounds, so its index number is 100.
- Index number for 2023 = (2.00 / 1.60) x 100.
- 2.00 / 1.60 = 1.25.
- Index number for 2023 = 1.25 x 100 = 125.
- Percentage increase = 125 - 100 = 25%.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A base year value is 40 and this year's value is 50. Find the index number.Show answer
Answer: 125 (50/40 x 100)
Q2An index number is 140 with a base value of 20. Find this year's value.Show answer
Answer: 28 (140/100 x 20)
Q3The price of milk was 0.80 pounds in the base year and 0.92 pounds this year. Find the index number for milk this year.Show answer
Answer: 115 (0.92/0.80 x 100)
Q4An item has an index number of 88 compared to its base year. State whether the value has increased or decreased, and by what percentage.Show answer
Answer: Decreased by 12% (100 - 88)
Q5A rent index shows 2019 = 100 and 2024 = 118. Find the actual rent in 2024 if the 2019 rent was 650 pounds.Show answer
Answer: 767 pounds (650 x 118/100)
Q6A cost index for electricity, relative to the same base year, was 120 in 2021 and 150 in 2023. Find the percentage increase in the cost of electricity from 2021 to 2023 (not from the base year).Show answer
Answer: 25% ((150-120)/120 x 100)
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A price index for petrol is 108 relative to a base year in which petrol cost 1.20 pounds per litre. Calculate the price of petrol in the given year.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
In 2010 (the base year) the cost of a school trip was 45 pounds. In 2024 the cost was 63 pounds. Calculate the index number for the cost of the trip in 2024, and state the percentage increase since 2010.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
A shop's cost index for a delivery service, using 2018 as the base year, is: 2018 = 100, 2020 = 112, 2022 = 126. (a) State the percentage increase in cost from 2018 to 2022. (b) Find the percentage increase in cost from 2020 to 2022.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the index numbers worksheet pack - 19 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 23 of GCSE Statistics Foundation Workbook 2 and chapter 30 of GCSE Statistics Higher Workbook 2, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on index numbers, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.