Difference between Interpolation and Extrapolation

1. Interpolation :
Interpolation refers to the estimation of a single value from two known values which are given from a sequence of values.

2. Extrapolation :
Extrapolation refers to the estimation of a single value from the given sequence of values where the background of values is known at certain times.

More precisely, we can define interpolation and extrapolation is as follows:

Suppose that we are given the following tabulated values of the function f(x) corresponding to a discrete set of values of x:

Interpolation is the process of finding the value of f(x) corresponding to any untabulated value of x between x₀ and x_n. The process of finding the value of f(x) for some value of x outside the given range  [x0, xn] is called extrapolation. It assumes that the behaviour of f(x) outside the given range is identical to the behaviour of f(x) inside the given range and this may not always be valid.

Difference between Interpolation and Extrapolation is as follows:

Sr. No.	Interpolation	Extrapolation
1.	Interpolation means reading a value which lies between two extreme points.	Extrapolation means reading a value which lies outside two extreme values.
2.	It supplies us the missing link.	It helps in forecasting.
3.	It refers to the insertion of an intermediate value in the series of terms.	It refers to projecting a value for the future.
4.	It can be calculated graphically. It is one of the simplest method of interpolation.	Graphic method is not applied for extrapolation.
5.	When records of some period are lost, figures relating to such projects may be estimated to complete the records by interpolation.	It plays significant role in economic planning. For economic planning, projection of future data is essential. This is done by extrapolation.
6.	It is the estimation of a most likely estimate in given conditions. The technique of estimating a past figure in termed as interpolation.	Estimating a probable figure for future is called extrapolation.
7.	Interpolation is preferred because we have a greater likelihood of obtaining a valid estimate.	In extrapolation, we are making the assumption that our observed trend continues for values of x outside the range. We used to form our model. This may not be the case. So we must be very careful while using extrapolation.