Interpolation and Extrapolation
Master Interpolation and Extrapolation for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. Interpolation predicts within the data range and is more reliable than extrapolation, which predicts beyond it.
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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.
Topic overview
A line of best fit can be used to estimate values, but the reliability of the estimate depends on where it falls relative to the data.
Interpolation estimates a value within the range of the data. It is reasonably reliable, because the line has been fitted using data on both sides of the point being estimated.
Extrapolation estimates a value beyond the range of the data. It is unreliable, because it assumes the trend continues outside the range where it was observed, and there is no evidence for that. The relationship may change, or may not hold at all in that region. Any answer involving extrapolation should state that the estimate may be unreliable.
Revision notes
Interpolation
Estimating a value within the range of the data collected.
Reasonably reliable, because the line was fitted using data points on both sides of the estimate. The correlation must also be reasonably strong for the estimate to be trusted.
Extrapolation
Estimating a value beyond the range of the data.
Unreliable, because it assumes the trend continues outside the range where it was observed. There is no evidence for that assumption, and the relationship may change or break down entirely.
Answering estimate questions
Read the value from the line, then comment on reliability.
State whether the estimate is interpolation or extrapolation, and say whether it is reliable and why. The comment usually carries a mark of its own.
Key points
- Interpolation estimates within the data range.
- Interpolation is reasonably reliable.
- Extrapolation estimates beyond the data range.
- Extrapolation is unreliable.
- It assumes the trend continues.
- Always comment on reliability.
Worked examples
Example 1
Data was collected for x between 10 and 50. An estimate is made at x = 30. State whether this is interpolation or extrapolation and comment on reliability. [2 marks]
Working
Example 2
Explain why extrapolation may give an unreliable estimate. [2 marks]
Working
Example 3
Data covers ages 20 to 60. An estimate is made for age 75. State the type of estimate and one concern. [2 marks]
Working
Common mistakes
Not checking whether the value is inside the data range.
That determines whether it is interpolation or extrapolation.
Extrapolating without commenting on reliability.
The comment usually carries a separate mark.
Saying interpolation is always accurate.
It is reasonably reliable, provided the correlation is strong.
Extending the line of best fit far beyond the data.
This makes the unreliability worse and should be avoided.
Exam tips
- Check the data range before making any estimate.
- Name the estimate as interpolation or extrapolation.
- Always comment on reliability.
- Note that strong correlation makes interpolation more trustworthy.
Key terms
- Interpolation
- Estimating within the range of the data.
- Extrapolation
- Estimating beyond the range of the data.
- Range of data
- The interval covered by the collected values.
- Reliable
- Likely to be close to the true value.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.