**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

6

10

20

36

50

**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

6

4

(10 - 6)

10

(20 - 10)

16

(36 - 20)

14

(50 - 36)

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

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.

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