Probability and Statistics > Statistics Definitions > Extrapolation

## What is Extrapolation?

Extrapolation is a way to make guesses about the future or about some hypothetical situation based on data that you already know. **Interpolation** allows you to estimate *within *a data set; it’s a tool to go beyond the data. It comes with a high degree of uncertainty. You’re basically taking your “best guess” based on facts you already know.

## Real Life Uses

You extrapolate to some degree in your daily life. For example, you might look forward to your monthly paycheck and you assume that you’re going to get it **based on known data** (the fact that you’ve got paid monthly, on-time for the last year). But what if your company goes bankrupt? Or the market crashes? Or the bank mistakenly freezes your bank account? In this particular case, extrapolation has a fair amount of certainty (you’re probably going to get your paycheck), but that isn’t always the case.

## Use in Statistics

Extrapolation can mean several things in statistics, but they all involve assumption and conjecture (extrapolation is far from an exact science!):

- The extension of a statistical method where you assume similar methods will be used.
- The projection, extension, or expansion of your known experience into an area that you do not know or that you haven’t experienced yet.
- The use of equations to fit data to a curve. You then use the equation to make conjectures. This is known as
**curve fitting**or regression, which can get quite complex, with the use of tools like the Correlation Coefficient.

### Other Practical Uses

Extrapolation is used in many scientific fields, like in chemistry and engineering where extrapolation is often necessary. For example, if you know the current voltages of a particular system, you can extrapolate that data to predict how the system might respond to higher voltages.

### Cautions with Use

In general, you should only extrapolate for small amounts of data. For example, you might be able to rely on a steady paycheck coming in for a few months or years, but it probably wouldn’t be a good idea to assume that same company is going to be still paying you 20 years down the road!

Thank you for explaining the concept of extrapolation!! It helped me a lot.