Interpolation Formula with Problem Solution & Solved Example

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Interpolation is the process of calculating a value between any two points or a curve. It helps us to look inside the data and it is useful not only in statistics but it is good for science, businesses, other useful studies too. It can predict values that lie between existing data points. Here is an example to help you with the concept of the interpolation.

A gardener planted one tomato plant measured its growth almost every passing day. Here, gardener is the curious person that would like to check the growth of tomatoes on the fourth day. The table of observations looked like this:

Day Height (mm)
1 0
3 4
5 8
7 12
9 16


Based on the observation, this is estimated that the growth of plant would be approximate 6mm at the fourth day. It happened because the plant is growing in a linear pattern and there exists a linear relationship between number of days and the growth of a plant. You can find the answers by plotting the values over a chart or graph.

But how to calculate the final answer of plant does not grow in a linear pattern. Here interpolation formula works the best way. Just plugin the values into formula and find the answer as needed.

Interpolation Formula

\[\large y=y_{1}+\frac{(x-x_{1})}{(x_{2}-x_{1})} \times (y_{2}-y_{1})\]

You just have to put the values in the interpolation formula as given above and find the output even if there exists non-linear relationship between data points. The formula can be used for linear pattern too and answer is still the same that was fund out with general calculations.