Question

The frequency distribution of marks obtained by students in a class test is given below. Draw frequency polygon and ogive.

Marks	0−10	10−20	20−30	30−40	40−50
Number of Students	5	10	14	10	3

Answer 1

In order to construct a frequency polygon without a histogram, we first calculate the mid-points corresponding to the class intervals. The mid-points are then plotted against their respective frequencies. The curve obtained on joining the points is the frequency polygon.

Marks	Mid Point	Students
0 − 10	$\frac{0+10}{2}=5$	3
10 − 20	$\frac{10+20}{2}=15$	10
20 − 30	$\frac{20+30}{2}=25$	14
30 − 40	$\frac{30+40}{2}=35$	10
40 − 50	$\frac{40+50}{2}=45$	3

In order to construct the ogives, we first need to calculate the less than and the more than cumulative frequencies as follows.

Marks	Cumulative Frequency
Less than 10 Less than 20 Less than 30 Less than 40 Less than 50	3 3 + 10 = 13 13 + 14 = 27 27 + 10 = 37 37 + 3 = 40

Marks	Cumulative Frequency
More than 0 More than 10 More than 20 More than 30 More than 40	40 40 − 3 = 37 37 − 10 = 27 27 − 14 = 13 13 − 10 = 3