Interpolation is the process of estimating unknown values that are inside the range of existing data.

Extrapolation is the process of estimating unknown values that are outside the range of existing data.

Interpolation versus extrapolation

Maths

In the prior unit, pupils explored different graphs and charts as a way of presenting data visually. Pupils were introduced to scatter graphs and learnt how to construct them. In this unit, this understanding is extended to using a line of best fit to allow interpolation.

Graphical representations of data: scatter graphs and time series

Interpolation is when you estimate values that are {{}} the range of available data.

Which values are obtained by extrapolation on this scatter diagram?

Select the regions where interpolation can be used to make estimations on this scatter graph.

No, extrapolation is always completely unreliable.

No, it can be used with caution as the trend might not continue.

Yes, extrapolation is always completely reliable.

Yes, you can make accurate predictions by extending your line of best fit.

Alex says, “I can always use extrapolation to make a valid prediction when my bivariate data has correlation.” Is Alex correct?

Aisha: I want the house price in Ashfield where the median income is £35 000

Jacob: I want the house price in the USA where the median income is £30 000

Jun: I want the house price in Oakford where the median income is £20 000

Sam: I want the house price in Elmway where the median income is £80 000

The scatter graph shows data taken from the ONS, where each point represents a region in England and Wales in 2023. Select which of these Oak pupils can use this graph to make an accurate prediction.

The scatter graphs shows information about house prices and income in different regions. Estimate the difference between the house prices in the North and South for a median income of £30 000

A {{ }} is a line where the distance between each data point and the line is minimised.

No, only lines of best fit for positive correlation go through the (0, 0).

No, the line of best fit depends on the distribution of the points.

Yes, when one variable is zero the other must be too.

Yes, it should always start in the bottom left corner of the graph.

Aisha says the line of best fit must always go through the point (0, 0). Is Aisha correct?

Which of these graphs do not have appropriate line of best fit?

The scatter graph shows data taken from the ONS, where each point represents a region in the UK. Use the line of best fit to estimate emissions of a population of 400 000

The scatter graph shows data taken from the ONS about regions in the UK. An estimate for the median house price in a region where the median income is £35 000 is £{{ }} to the nearest thousand.

The scatter graph shows data taken from the ONS about regions in the UK. The population of a region is predicted to change from 200 000 to 500 000. Estimate how many more cell towers the region needs.

This lesson will be removed by end of Summer Term 2025.

Interpolation versus extrapolation

Lesson outcome

This lesson will be removed by end of Summer Term 2025.