Extrapolation‌

We can simply define extrapolation as an estimation. But the condition is estimating the overall value further than the range of values.

It is one of the most important in the field of statistics. It is not just limited to statistics; it is also used widely in other fields like engineering, data categorization, psychology, and many other scientific fields.

Extrapolation means understanding unknown values by using known values. Thus, predicting future data using the history of data.

Let’s consider an example to understand extrapolation. Let a₁, a₂,………a₅₀ be the known data. And if we need to find the point a₅₁ by using the known data, then that point(a₅₁) is said to be the extrapolation point.

We use extrapolation in our daily usage. Wondering how? When you want to travel from one place to another place in a vehicle, we will think of a route whether it is safe to go or not.

Exploration Statistics

As we already discussed, extrapolation plays an important role in statistics because of its concept of estimating the future.

If we take an example of a current company's stats, size of the population, etc., using extrapolation statistics results in estimating the growth or downfall of the company and increase or decrease in size of the population in the future.

Methods Of Extrapolation

Extrapolation is mainly classified into three (3) categories which as discussed below:

• Linear Extrapolation
• Polynomial Extrapolation
• Conic Extrapolation

1. Linear Extrapolation

Linear extrapolation using a linear equation or function gives good results when the predicted value is close to the available data. It is done by drawing a tangent line at the endpoints of the graph, expanding it beyond the limits.

2. Conic Extrapolation

A conic section is obtained by using five points that are near to the given data. If it is a circle or ellipse, then the conic section curves back itself. But in the case of a parabolic or hyperbolic curve, it may not curve back to itself as it is relative to the x-axis.

3. Polynomial Extrapolation

The curve of the polynomial can be drawn using known values or near endpoints. The process is done by using Lagrange interpolation or Newton's system of finite series to have the data. The resulting polynomial can be used in extrapolating the data.

Formula Of Extrapolation

Calculation of linear exploration using two endpoints (x1, y1) and (x2, y2) in the linear graph when the value of point to be extrapolated is x, then a formula that can be used is as follows:

Example 1: Given points in a straight line are (2, 3) and (4, 5).Find the value of y at x = 7 on the straight line by using the method of linear extrapolation.

Solution:

Given, x₁=2, y₁=3

x₂=4, y₂=5

Therefore, linear extrapolation is given by,