Interpolation means: given a set of data points, you fill in between data points. Sometimes, you only have sample data. And, you want to fit a nice looking curve on this sample. You can interpolate what data will be for "missing" values, which is strictly in between sample data points according to a topological time order. Therefore, you fill in the blanks. This is called Interpolation.
Extrapolation is also filling in the blanks, but the blanks are in distant future. You are in a way forecasting or predicting what data may look like, given past data. You are doing this, because you want to understand the unknown, or come up with an explanation for the unknown. This is called Extrapolation.
If you look ahead, you extrapolate. If you look back and reflect, you interpolate.
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