You have data at some points but you want data at other points. Maybe you have sales data at irregular intervals and want to straighten it out to regular weekly intervals. Or maybe some of your data is missing and you’d like to fill in the gaps as accurately as you can. Or maybe you have data for scattered cities and want to fill in values for cities in between.

If you have data around the point where you want it, that’s **interpolation**. If you want to project beyond where you have data, such as in forecasting, that’s **extrapolation**.

## Simple interpolation

Interpolation and extrapolation can be very simple. For example, if you just have data at two points and want to fill in the value at a third point, you could use this online calculator.

## More complex interpolation

But things can quickly get more complicated. Maybe you have geographical data, and you’re trying to fit a **surface** and not just a **curve**. Maybe your data are so far spread that **you can’t ignore that the earth is round**. Or maybe you have data in three or more dimensions.

Maybe you want your interpolation to have certain nice properties, and so you want to use cubic splines, Bézier curves, Chebyshev polynomials, etc. Or maybe you have a list of **constraints** you have to satisfy while you’re doing your interpolation.

## Statistical inference

You’d probably like to know not just how to fill in missing values but also to have some idea how accurate the filled in value is. Then you’re going beyond interpolation and extrapolation per se and getting into statistical regression.

## Expert help

If you’d like help with an interpolation or extrapolation problem, we can help. And if you decide that you really have a statistical problem, we can help with that too. Please call or email to discuss your project.

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