AI generatedStatisticsKS3 / GCSE

Explaining the risk of extrapolation

Explaining the risk of extrapolation.

  • Plot paired observations as separate crosses. Do not join the points.
  • A best-fit line follows the overall trend, with points balanced around it.
  • Predictions are estimates. Extrapolation is less secure, and correlation alone does not establish causation.

Example 1

Explain why this prediction may be unreliable. Use the shown line of best fit to predict when .

Coordinate graph1234567891011510152025300
Go vertically to the line, then horizontally to the -axis.This is extrapolation: outside the observed -values, where the trend may change.
. Use caution: the pattern is not known to continue beyond the data.

Example 2

Explain why this prediction may be unreliable. Use the shown line of best fit to predict when .

Coordinate graph12345678910115101520250
Go vertically to the line, then horizontally to the -axis.This is extrapolation: outside the observed -values, where the trend may change.
. Use caution: the pattern is not known to continue beyond the data.

Your turn

Question 1

Explain why this prediction may be unreliable. Use the shown line of best fit to predict when .

Coordinate graph123456789101151015202530350
Check answer
Go vertically to the line, then horizontally to the -axis.This is extrapolation: outside the observed -values, where the trend may change.
. Use caution: the pattern is not known to continue beyond the data.
Question 2

Explain why this prediction may be unreliable. Use the shown line of best fit to predict when .

Coordinate graph12345678910115101520250
Check answer
Go vertically to the line, then horizontally to the -axis.This is extrapolation: outside the observed -values, where the trend may change.
. Use caution: the pattern is not known to continue beyond the data.
Question 3

Explain why this prediction may be unreliable. Use the shown line of best fit to predict when .

Coordinate graph123456789101151015202530350
Check answer
Go vertically to the line, then horizontally to the -axis.This is extrapolation: outside the observed -values, where the trend may change.
. Use caution: the pattern is not known to continue beyond the data.
Question 4

Explain why this prediction may be unreliable. Use the shown line of best fit to predict when .

Coordinate graph12345678910115101520250
Check answer
Go vertically to the line, then horizontally to the -axis.This is extrapolation: outside the observed -values, where the trend may change.
. Use caution: the pattern is not known to continue beyond the data.
Question 5

Explain why this prediction may be unreliable. Use the shown line of best fit to predict when .

Coordinate graph1234567891011510152025300
Check answer
Go vertically to the line, then horizontally to the -axis.This is extrapolation: outside the observed -values, where the trend may change.
. Use caution: the pattern is not known to continue beyond the data.
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