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Interpolation and Extrapolation

In this worksheet, students practice interpolation and extrapolation in scatter diagrams

'Interpolation and Extrapolation' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Statistics

Curriculum subtopic:   Statistics Analysing Data

Difficulty level:  

Worksheet Overview

When dealing with scatter diagrams, the questions in a GCSE paper follow a structure that is usually the same year in year out.

1) Draw the scatter graph

2) Comment on the correlation/relationship

3) Read the scatter graph

4) Comment on the scatter graph

 

In this activity, we're going to look at the last two.

 

Interpolation vs Extrapolation.

The difference between these two words is actually quite simple.

Interpolation is where you use the line of best fit for a value that is within the plotted points

Extrapolation is where you use the line of best fit for a value that is outside the plotted points (You have extended the pattern)

 

The danger of extrapolation

When you are drawing a line of best fit, we draw a straight line through the points and use this to read values.

The problem here is we don't actually know what happens outside the points we are given. How do we know that the graph doesn't take a sudden upwards turn? How do we know it doesn't flatten out? or turn downwards?

Because of this, we have to be very wary of using extrapolated values.

 

How would this be phrased in an exam?

The common way this is phrased would be along the lines of...

'James wants to use this scatter graph to predict the height of a man who weighs 100 kg, explain why this could give a result that isn't accurate.'

The answer to this will always be...

'He is using a value outside of the points that I have plotted'

You don't even have to use the word extrapolated.

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