If data is ordered ascending, e.g.:

A B
1 1
2 3
3 5
5 7
7 13

The following formula interpolates any value in the range:

=PERCENTILE(B1:B5,PERCENTRANK(A1:A5,C1,20))

Or if you want to use a "best fit" line for extrapolating try:

=FORECAST(C1,B1:B5,A1:A5)

with C1 as 6.5 the two formulas return 11.5 and 11.25 respectively.

Phil wrote:
Is there a function or method of programming which can be used to interpolate
or extrapolate values from a table?