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Index Numbers

FoundationHigherAQAEdexcel

Learn Index Numbers for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. An index number compares a value with a base value, which is set at 100.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

An index number compares a quantity at one time with its value at a base time, expressed as a percentage.

The formula is \(\text{index} = \frac{\text{current value}}{\text{base value}} \times 100\). The base year always has an index of 100, because the current and base values are equal.

An index above 100 shows an increase since the base year and an index below 100 a decrease. An index of 115 means a 15 per cent increase; an index of 92 means an 8 per cent decrease. Subtracting 100 from the index gives the percentage change directly, which is the quickest way to interpret one.

Revision notes

The formula

\(\text{Index} = \frac{\text{current value}}{\text{base value}} \times 100\).

The base year has an index of 100 by definition, since its current and base values are the same.

Interpreting an index

Above 100 means an increase since the base year; below 100 means a decrease.

Subtract 100 to get the percentage change directly. An index of 115 is a 15 per cent increase; an index of 92 is an 8 per cent decrease.

Working backwards

To find a current value from an index: current value \(= \frac{\text{index}}{100} \times \text{base value}\).

This requires the base value to be known. Without it, only the proportional change can be found, not the actual figure.

Key points

  • An index compares a value with a base value.
  • \(\text{Index} = \frac{\text{current}}{\text{base}} \times 100\).
  • The base year always has an index of 100.
  • Above 100 means an increase.
  • Below 100 means a decrease.
  • Index minus 100 gives the percentage change.

Worked examples

Example 1

A price rises from £40 to £46. Work out the index number using £40 as the base. [2 marks]

Working

\(\frac{46}{40} \times 100\)divide the current value by the base value and multiply by 100
\(= 115\)work out the index

Example 2

An index number is 92. Interpret this. [2 marks]

Working

\(92 - 100 = -8\)subtract 100 from the index
so the value has decreased by 8 per cent since the base yearstate the interpretation

Example 3

A base value is £250 and the index is 124. Work out the current value. [2 marks]

Working

\(\frac{124}{100} \times 250\)divide the index by 100 and multiply by the base value
\(= £310\)work out the current value

Common mistakes

  • Forgetting to multiply by 100.

    The index is a percentage, so the ratio must be multiplied by 100.

  • Inverting the fraction.

    It is current divided by base, not the other way round.

  • Saying an index of 115 means 115 per cent increase.

    It means a 15 per cent increase — subtract 100 first.

  • Giving the base year an index other than 100.

    By definition the base year index is always 100.

Exam tips

  • Write the formula before substituting.
  • Subtract 100 to interpret the percentage change.
  • Check the base year has an index of 100.
  • Keep current on top of the fraction.

Key terms

Index number
A value comparing a quantity with a base value.
Base year
The reference year, given an index of 100.
Percentage change
The index minus 100.
Base value
The value in the base year.

Related topics

Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.