Interpolation versus extrapolation | Maths | Quizalize & Oak National Academy

Starter quiz

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

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

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.
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

500 kt CO2e

550 kt CO2e ✓

750 kt CO2e

500 000 kt CO2e

550 000 kt CO2e
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.

'450 000' ✓
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.

2000

4000

7000 ✓

9000

11 000

Exit quiz

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

'inside' ✓
Which values are obtained by extrapolation on this scatter diagram?

A

B ✓

C

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

A only

B only ✓

C only

A and C

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

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.
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.

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 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

£100 000

£125 000 ✓

£175 000

£250 000

£375 000

Worksheet

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Lesson Details

Key learning points

Interpolation can be used to estimate a value within the data set.
Extrapolation can be used to estimate a value outside of the data set.
Extrapolation may not be valid as this is outside observed set of data values.
Interpolation may not be valid due to the limitations of sampling.

Common misconception

Interpolation and extrapolation always produce accurate predictions.

Extrapolation may not be valid as this is outside the observed set of data values (e.g. a linear trend might not continue indefinitely). Interpolation may not be valid due to the limitations of the data set.

Keywords

Interpolation - Interpolation is the process of estimating unknown values that are inside the range of existing data.
Extrapolations - Extrapolation is the process of estimating unknown values that are outside the range of existing data.