Skip to content
VirtusAcademy

Chain Base Index Numbers

HigherHigher tier onlyAQAEdexcel

Revise Chain Base Index Numbers for GCSE Statistics with this free worksheet and full mark scheme — Higher tier exam-style questions with worked answers for AQA and Edexcel. A chain base index compares each value with the previous period rather than a fixed base year.

Free downloads

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.

This is a Higher tier only topic, so there's no Foundation paper — only the Higher worksheet and mark scheme below.

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

A chain base index compares each value with the previous period rather than with a fixed base year. This is a Higher-only topic.

The formula is \(\frac{\text{this year's value}}{\text{previous year's value}} \times 100\). Each index therefore measures the change over one period only.

The advantage is that it shows year-on-year change directly, making it easy to see whether growth is speeding up or slowing down. The disadvantage is that values from different years cannot be compared with each other, because each has a different base — an index of 105 one year and 105 the next means two successive 5 per cent rises, not no change.

Revision notes

The formula

Chain base index \(= \frac{\text{this year's value}}{\text{previous year's value}} \times 100\).

Each index measures the change over a single period, comparing with the year immediately before rather than a fixed base.

Advantages

It shows year-on-year change directly.

This makes it easy to see whether growth is accelerating or slowing, which a fixed base index does not show as clearly.

Disadvantages

Values from different years cannot be compared with each other, because each has a different base.

An index of 105 followed by another 105 means two successive 5 per cent rises, not no change. This is the point most often misinterpreted.

Key points

  • A chain base index compares with the previous period.
  • \(\frac{\text{this year}}{\text{previous year}} \times 100\).
  • Each index covers one period only.
  • It shows year-on-year change directly.
  • Different years cannot be compared with each other.
  • Each year has a different base.

Worked examples

Example 1

A value rises from 250 to 275. Work out the chain base index. [2 marks]

Working

\(\frac{275}{250} \times 100\)divide this year's value by last year's and multiply by 100
\(= 110\)work out the index

Example 2

Chain base indices for two successive years are both 104. Explain what this shows. [2 marks]

Working

Each year the value rose by 4 per cent compared with the year beforeinterpret each index
so there were two successive 4 per cent rises, not no change over the two yearsstate the overall effect

Example 3

Give one advantage of a chain base index over a fixed base index. [1 mark]

Working

It shows the year-on-year change directly, making it easy to see whether growth is speeding up or slowing downgive the advantage

Common mistakes

  • Comparing chain base indices from different years.

    Each has a different base, so they cannot be compared directly.

  • Reading two equal indices as no change.

    Two indices of 105 mean two successive 5 per cent rises.

  • Using a fixed base value.

    The base is the previous year's value, which changes each time.

  • Inverting the fraction.

    This year's value goes on top.

Exam tips

  • Use the previous year as the base each time.
  • Interpret each index as a one-period change.
  • Never compare chain base indices across years.
  • Remember this is a Higher-only topic.

Key terms

Chain base index
An index comparing with the previous period.
Fixed base index
An index comparing with a single base year.
Year-on-year change
The change from one year to the next.
Base
The value being compared against.

Related topics

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