Method of Constructing a Frequency Polygon with the Help of a Histogram

We will discuss about the method of constructing a frequency polygon with the help of a histogram.

Step I: Draw the histogram for the frequency distribution as explained above.

Step II: Locate the midpoint of the top horizontal side of each rectangle in the histogram.

Step III: Locate the middle points on the horizontal axis of two imaginary intervals of common size, one before the first class interval and the other after the last class interval.

Step IV: Join all the above midpoints by line segments one after the other in order.

Example: Draw the frequency polygon for the following frequency distribution.

Marks Obtained

Under 20

Under 40

Under 60

Under 80

Under 100

Number of Students






Solution: Changing the distribution into a continuous distribution of overlapping intervals, we have the following table.

Marks Obtained

0 - 20

20 - 40

40 - 60

60 - 80

80 - 100

Number of Students



(10 - 6)


(20 - 10)


(36 - 20)


(50 - 36)

The histogram of the distribution is shown in the adjacent figure.

Method of Constructing a Frequency Polygon with the Help of a Histogram

Following steps II, III and IV, the frequency polygon will be as shown alongside.

Scale: On the x-axis, 1 cm = 20 marks.

On the y-axis, 2 mm = 1 student.

10th Grade Math

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