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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:

Match each term to its meaning

  • 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

An interactive activity.

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

An interactive activity.

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

An interactive activity.

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

An interactive activity.

Explain an index

An interactive activity.