# What is the difference between extrapolation and interpolation?

Extrapolation and interpolation are two techniques used in data analysis, and they have significant differences in their approach and results.

Extrapolation involves estimating values beyond the range of the given data, i.e., predicting data outside of the observed range. Extrapolation is useful when we want to make predictions based on trends or patterns that are outside of the observed range. However, it is risky because we are making assumptions about the data that are not based on actual observations.

For example, suppose we have a dataset of house prices in a city for the last ten years, and we want to predict the prices for the next five years. Extrapolation would involve predicting the prices beyond the observed range, and it can be challenging to estimate accurately.

Interpolation, on the other hand, involves estimating values between the observed data points. In other words, it is the process of estimating the value of a function at a point within the range defined by the data. Interpolation is useful when we want to estimate a value between two known data points or to smooth out noise in the data.

For example, suppose we have a dataset of monthly rainfall in a city for the last ten years, and we want to estimate the rainfall for a particular month that is missing from the dataset. Interpolation would involve estimating the rainfall value for that month based on the observed data.

In summary, extrapolation is used to predict values outside the observed range of data, while interpolation is used to estimate values between the observed data points. Extrapolation is risky because it relies on making assumptions about the data, while interpolation can be useful for smoothing out noise in the data or estimating missing values.