Extrapolation — Grade 8 Math, what it means and where it is taught
Predicting outside the range. Risky.
Taught in Grade 8 Math.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Range — The set of outputs that actually occur.
Practise this idea
3 questions in the course bank use Extrapolation, in Lines of Best Fit, Bivariate Data & Correlation.
Problem 1
Data covers x from 2 to 15. Predicting at x = 80 is
- extrapolation, and unsafe
- interpolation, and safe
- impossible to compute
- the same as the mean
Worked answer
extrapolation, and unsafe
80 is far outside 2 to 15
That is extrapolation
The pattern may not continue
Problem 2
A best-fit line for a child's height against age gives y = 2.4x + 30 inches. Predict the height at age 40 and say whether to trust it.
Worked answer
126 inches, not trustworthy
2.4(40) + 30 = 126 inches
That is over 10 feet
Far outside the data range, so an unsafe extrapolation
Problem 3
A regression on data for x between 5 and 20 gives y = 3x + 10. Is predicting at x = 200 reliable? Answer yes or no.
Worked answer
no
200 is far outside 5 to 20
That is extrapolation
So not reliable