Finding Mode Graphically

Marks
inclusive series
Conversions into
exclusive series
No. of students
(frequency)
(x)   (f)
10-19 9.5-19.5 10
20-29 19.5-29.5 12
30-39 29.5-39.5 18
40-49 39.5-49.5 30
50-59 49.5-59.5 16
60-69 59.5-69.5 6
70-79 69.5-79.5 8

The following steps must be followed to find the mode graphically.

1. Represent the given data in the form of a Histogram.The hight of the rectangles in the histogram is marked by the frequencies of the class interval as shown in the graph .Identify the highest rectangle. This corresponds to the modal class of the series.

2. Join the top corners of the modal rectangle with the immediately next corners of the adjacent rectangles. The two lines must be cutting each other.This might be difficult to visualise so look at the graph given below.

3. Let the point where the joining lines cut each other be 'A'. Draw a perpendicular line from point A onto the x-axis. The point 'P' where the perpendicular will meet the x-axis will give the mode.

The Histogram

In this case the value of point P turns out to be 44.12