Index Numbers - Worksheets, Questions and Revision

18 original exam-style questions - 14 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Statistics

S13 Index Numbers

EDEXCEL 1ST0 · Calculator allowed · about 85 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A bakery uses 2018 as the base year to track the price of a pack of bread rolls. In 2018 (the base year), a pack of bread rolls cost £1.40. In 2023, the same pack cost £1.75.

index number = (price in a given year / price in the base year) x 100
(a)Write down the index number for the base year, 2018.(1)
(b)Calculate the index number for the price of bread rolls in 2023.(2)
(c)Write down whether the price of bread rolls has increased or decreased between 2018 and 2023, and explain how you know.(1)
(Total for Question 1 is 4 marks)
2
A hairdresser uses 2019 as the base year for the price of a standard haircut. In 2019, a haircut cost £18. Using 2019 as the base year, the index number for the price of a haircut in 2024 is 130.
(a)Explain what an index number of 130 tells you about the price of a haircut in 2024, compared with 2019.(1)
(b)Work out the price of a haircut in 2024.(2)
(Total for Question 2 is 3 marks)
3
A council uses 2017 as the base year to track the daily fee for parking in the town centre car park. In 2017, the daily fee was £6.00. Using 2017 as the base year, the index number for the daily fee in 2021 is 90.
(a)Write down whether the daily parking fee increased or decreased between 2017 and 2021, and explain how you know.(1)
(b)Work out the daily parking fee in 2021.(2)
(c)Work out the percentage decrease in the daily parking fee from 2017 to 2021.(1)
(Total for Question 3 is 4 marks)
4
For each statement about index numbers, write down whether it is True or False.
(i)The base year for an index number is chosen by the person constructing the index, and can be any year.(1)
(ii)Index numbers can only be used to track prices, and cannot be used for other quantities such as population or sales.(1)
(iii)If an index number for a given year is greater than 100, the quantity being measured has increased since the base year.(1)
(iv)Index numbers are given in the same units as the original data, such as pounds (£) or kilograms.(1)
(Total for Question 4 is 4 marks)
5
Four items, W, X, Y and Z, each have an index number for this year, all using the same base year (=100):
ItemIndex number
W104
X96
Y122
Z100
(a)Which item has stayed at exactly the same price as in the base year?(1)
(b)Which item is the only one to have decreased in price since the base year?(1)
(c)Which item has had the greatest percentage increase in price since the base year, and what is that percentage increase?(2)
(Total for Question 5 is 4 marks)
6
An allotment society uses 2015 as the base year for the annual rental fee of a standard plot.
YearRental fee (£)
2015 (base year)40.00
201946.00
202352.00
(a)Show that the index number for the rental fee in 2019 is 115.(2)
(b)Work out the index number for the rental fee in 2023.(2)
(c)Write down which of the two years, 2019 or 2023, saw the bigger percentage increase in the rental fee since 2015.(1)
(Total for Question 6 is 5 marks)
7
A film streaming service uses 2020 as the base year for its monthly subscription price.
YearSubscription price (£)
2020 (base year)6.00
20226.90
20237.50
20258.40
(a)Calculate the index number for the subscription price in 2022.(2)
(b)Calculate the index number for the subscription price in 2023.(2)
(c)Calculate the index number for the subscription price in 2025.(2)
(d)Write down the first year shown in the table in which the subscription price index exceeded 120.(1)
(Total for Question 7 is 7 marks)
8
A telecoms company uses 2016 as the base year for the price of its standard monthly broadband subscription. The table shows the fixed-base index number for the subscription price in two later years (2016 = 100).
YearFixed-base index number (2016 = 100)
2020112
2024126
(a)Write down the percentage increase in the subscription price from 2016 to 2020.(1)
(b)Work out the percentage increase in the subscription price from 2020 to 2024.(3)
(c)Explain why the percentage increase from 2020 to 2024 cannot be found simply by subtracting the index numbers (126-112=14) and treating this as a percentage.(2)
(Total for Question 8 is 6 marks)
9
The Retail Price Index (RPI) measures the average change in the prices of a range of goods and services bought by households. The table shows the RPI for three years, using 2018 as the base year.
YearRPI (2018 = 100)
2018 (base year)100
2022115
2024121
(a)Write down what an RPI of 115 in 2022 tells you about average prices, compared with 2018.(1)
(b)A charity gives a fixed £200 prize each year from 2018 to 2024, without increasing it in line with the RPI. Explain whether the £200 prize is worth more, or less, in real terms in 2024, compared with 2018.(2)
(c)Work out how much the charity would need to give as the prize in 2024, if it wanted the prize to have kept pace with the RPI since 2018.(2)
(Total for Question 9 is 5 marks)
10
Two market stalls, Stall A and Stall B, each use 2020 as the base year for the price of their most popular item. In 2024, Stall A's item had a price index number of 132, and Stall B's item had a price index number of 121.
(a)Write down which stall's item has increased in price by the greater percentage since 2020.(1)
(b)Stall A's item cost £5.00 in 2020. Stall B's item cost £8.00 in 2020. Work out the price of each stall's item in 2024.(4)
(c)State which stall's item is more expensive in 2024, and explain why this is not the stall identified in part (a).(2)
(Total for Question 10 is 7 marks)
11
A fixed-base index number always compares a value with a single, fixed base period. A chain-base index number compares each period only with the period immediately before it.

For each statement, write down whether it is True or False.
(i)A fixed-base index number for 2024 (using 2015 as the base year) compares the 2024 value directly with the 2015 value.(1)
(ii)A chain-base index number for 2024 compares the 2024 value with the value in 2015, the original base year.(1)
(iii)For the same data, a chain-base index number for a particular year is usually a different value from the fixed-base index number for that same year.(1)
(Total for Question 11 is 3 marks)
12
A fuel station uses 2019 as the base year for the price of one litre of unleaded petrol. In 2019, one litre cost £1.25. The table shows the index number for the petrol price in three later years.
YearIndex number (2019 = 100)
202092
2021108
2023116
(a)Write down which year had the lowest petrol price compared with the base year.(1)
(b)Work out the price of one litre of petrol in 2020.(2)
(c)Work out the percentage increase in the petrol price from 2020 to 2023.(2)
(Total for Question 12 is 5 marks)
13
A farm shop records the price of a box of eggs at the start of each month.
MonthPrice of a box of eggs (£)
January2.00
February2.20
March2.42

A fixed-base index number compares each month with a single fixed base month. A chain-base index number compares each month only with the month immediately before it:

chain-base index number = (this month's price / previous month's price) x 100
(a)Using January as the fixed base month, work out the fixed-base index number for March.(2)
(b)Work out the chain-base index number for February, compared with January.(2)
(c)Work out the chain-base index number for March, compared with February.(2)
(d)State one advantage of using a chain-base index, rather than a fixed-base index, to track the egg price from month to month.(1)
(Total for Question 13 is 7 marks)
14
A school wants to track how the cost of hiring a coach for the annual Year 10 geography trip has changed over time, by building a simple price index. It plans to follow the statistical enquiry cycle.
(a)(Plan) State one decision the school must make before it can build a fixed-base index for the coach hire cost.(1)
(b)(Collect) The school could get one coach hire quote each year from a single company, or collect quotes from several companies each year and use the average. Give one reason why using the average of several companies' quotes gives a more reliable index.(1)
(c)(Process) The school used 2019 as the base year, when the average coach hire quote was £360. In 2024, the average quote was £441. Calculate the index number for the coach hire cost in 2024.(2)
(d)(Interpret) Interpret the index number found in part (c) in the context of the coach hire cost.(1)
(e)(Evaluate) The school only tracked the coach hire cost, but the total cost of the trip also includes entry fees and food. Suggest one improvement the school could make to better track the overall cost of the whole trip using index numbers.(1)
(Total for Question 14 is 6 marks)
15
A student is calculating an index number for the price of a magazine. The magazine cost £2.50 in the base year and £3.25 this year. The student's working is shown:

Step 1: 3.25 - 2.50 = 0.75
Step 2: index number = 0.75

The correct index number for the magazine is actually 130.
(a)Identify the student's error, and use the correct method to show that the correct index number is 130.(3)
(b)A second student says: 'Since the index number is 130, the magazine now costs £1.30 more than in the base year.' Explain why this statement is incorrect, and state the correct increase in price.(2)
(Total for Question 15 is 5 marks)
16
A worker's annual wage index (2017 = 100) was 124 in 2024. Over the same period, the price index for the worker's cost of living (2017 = 100) was 118 in 2024.
(a)Write down the percentage increase in the worker's wage from 2017 to 2024.(1)
(b)Write down the percentage increase in the cost of living over the same period.(1)
(c)Explain whether the worker is better off, worse off, or in the same position in real terms in 2024, compared with 2017.(2)
(Total for Question 16 is 4 marks)
17
A garden centre uses a certain year as the base year for the price of a particular garden bench. Using that (original) base year, the index number for the bench's price in 2021 was 108, and the index number for the same bench's price in 2024 was 126.
(a)Work out the index number for the bench's price in 2024, using 2021 (instead of the original base year) as the new base year. Give your answer correct to 1 decimal place.(3)
(b)The bench cost £150 in 2021. Work out the price of the bench in 2024.(2)
(c)Explain why it was possible to work out the answer to part (b) without knowing the bench's price in the original base year.(1)
(Total for Question 17 is 6 marks)
18
Two towns, Elmswood and Norbury, each publish a chain-base index number for average house prices over three years (each year compared with the year before it).
YearElmswood chain-base indexNorbury chain-base index
2022108104
2023104102
2024102108
(a)Work out Elmswood's overall fixed-base index number for 2024, with 2021 as the base year (2021 = 100), by combining its three chain-base index numbers. Give your answer correct to 1 decimal place.(2)
(b)Work out Norbury's overall fixed-base index number for 2024, with 2021 as the base year (2021 = 100), by combining its three chain-base index numbers.(2)
(c)A resident says: 'Elmswood and Norbury had different chain-base index numbers in each individual year, so their overall change in house prices over the three years must also be different.' Use your answers to parts (a) and (b) to evaluate this claim.(3)
(Total for Question 18 is 7 marks)
Mark scheme · S13 Index Numbers

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18