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 

1061_graphical method.png

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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