## Graphical method for interpolation, Mathematics

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Graphical Method

While drawing the graph on a natural scale, the independent variables are marked along the horizontal line and corresponding dependent variables are taken as ordinates. The points so plotted are joined by a smooth curve. For interpolation, the value of the independent variable is marked at the proper place on the X-axis and a line perpendicular to the X-axis is drawn from the point so marked to intersect the curve. Again by drawing a line perpendicular to the Y-axis from the point of intersection on the curve to meet the Y-axis, the value of the dependent variable is ascertained by reading off the value at the point of intersection with the Y-axis. The illustration given below demonstrates the use of this method.

Example

The population of a town is as follows:

Figure Year 1941 1951 1961 1971 1981 1991 Population (in 000's) 24 30 40 54 78 104

Find the population for the years 1976 and 1978.

Marking points on the X-axis, for the years 1976 and 1978, and dropping perpendiculars, the population for the years can be interpolated as 65,000 and 70,000 respectively.

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