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.