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Index Numbers and Rates of Change

Compare data over time: work out index numbers against a base year, read what they mean, and calculate rates of change like house prices and birth rates.

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What you'll cover

Comparing over time

Index numbers and rates of change let us compare data over time. An index number compares a value to a base year; a rate of change measures how fast something rises or falls. You meet both in real measures like the cost of living.

Key terms

Learn these before you begin:

RPI against CPI

  • Index number
  • Base year
  • RPI
  • CPI
  • A value compared to a base year set to 100
  • The starting year, set to 100
  • The Retail Prices Index
  • The Consumer Prices Index

Working out an index number

To find an index number, divide this year value by the base-year value, then multiply by 100: index = (value / base-year value) x 100 The base year always has an index of 100. An index above 100 means a rise; below 100 means a fall.

Calculate the index

In the base year, a basket of goods cost £40. This year the same basket costs £50. What is the price index this year? Use index = value / base-year value x 100.

Reading an index

A price index is 120. What does that tell you compared with the base year?

  • Prices have risen by 20%
  • Prices have fallen by 20%
  • Prices have risen by 120%
  • Prices have not changed

Rates of change

A rate of change measures how much something rises or falls, often as a percentage: rate of change = (change / original value) x 100 Rates are used for house prices, wages, births, deaths and unemployment. A crude rate per 1000, such as a birth rate, uses (count / population) x 1000.

Calculate the rate

A town's average house price rose from £200,000 to £220,000. What is the percentage rate of change? Use rate = change / original x 100.

Real measures

Select the TWO real measures that are index numbers or rates used in statistics.

  • The Retail Prices Index
  • The Consumer Prices Index
  • The average height of a class
  • The colour of a car

Calculate the birth rate

A country has 500,000 people, and 8,000 babies are born in a year. What is the crude birth rate per 1000 people? Use rate = births / population x 1000.

Index and rate frame

An index number compares a value to a _____ year, which is set to _____. An index of 130 means a rise of _____ percent. A rate of change is the _____ divided by the original value, times 100.

base 100 30 change mean 50 13 total

Match each index value to what it means

  • Index of 100
  • Index of 120
  • Index of 90
  • Index of 105
  • The base year, no change
  • A 20% rise
  • A 10% fall
  • A 5% rise

Apply it

Apply index numbers and rates of change to each situation.

  • A price index this year is 100. Compared with the base year, prices have...
  • Wages rose from £500 to £550 a week. The rate of change is...
  • An index number below 100 tells you the value has...

Explain an index

A shop's price index has risen from 100 to 115 over five years. Explain what this means and how you would work out the percentage rise.

  • Say what the base-year index of 100 represents
  • State the percentage rise
  • Explain how you calculated it (change / base x 100)