Index numbers (AQA GCSE Statistics): Revision Notes

Index numbers

Index numbers are a mathematical tool used to track how values change over time. Think of them as a special type of percentage that helps us compare prices, costs, or other values from different time periods. They're particularly useful in economics and statistics for measuring things like inflation, price changes, and investment growth.

What are index numbers?

Index numbers work by comparing current values to a reference point called the base year. The base year is always given an index number of 100, which represents the starting point for all comparisons. This makes it easy to see whether values have increased or decreased over time.

When an index number is:

• More than 100: The value has increased since the base year
• Exactly 100: The value is the same as in the base year
• Less than 100: The value has decreased since the base year

For example, if a laptop cost £500 in 2010 (the base year) and £425 in 2016, we can see that the price has fallen because the index number would be less than 100.

Calculating an index number

When you need to find an index number, you're essentially working out how much a value has changed compared to the base year. The formula for calculating an index number is:

$\text{Index number} = \frac{\text{cost in year n}}{\text{cost in base year}} \times 100$

Let's work through this step by step using a laptop price example:

Using an index number to find costs

Sometimes you'll know the index number and need to work backwards to find the actual cost or price. This is where the reverse formula comes in handy:

$\text{Cost in year n} = \text{cost in base year} \times \frac{\text{new index number}}{100}$

This formula is particularly useful for calculating how investments or prices have changed over time.

Worked examples

Key formulas to remember

Common exam tips

Remember!