Question

From the following frequency distribution, obtain the (i) ‘less than’ series and (ii) ‘more than’ series.

Marks obtained	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Number of students	7	11	9	25	8

Answer 1

Given: Marks obtained: 0 – 10, 10 – 20, 20 – 30, 30 – 40, 40 – 50

Number of students (frequencies): 7, 11, 9, 25, 8

Step-wise calculation:

1. Compute the “less than” series (cumulative from lowest class upward):

Less than 10 = frequency of 0 – 10 = 7

Less than 20 = 7 + 11 = 18

Less than 30 = 18 + 9 = 27

Less than 40 = 27 + 25 = 52

Less than 50 = 52 + 8 = 60 (total N = 60)

2. Compute the “more than” series (cumulative from highest class downward):

More than 40 = frequency of classes above 40 (i.e., 40 – 50) = 8

More than 30 = 8 + 25 = 33

More than 20 = 33 + 9 = 42

More than 10 = 42 + 11 = 53

More than 0 = 53 + 7 = 60 (total N = 60)

(i)

Marks (less than)	No. of students
10	7
20	18
30	27
40	52
50	60

(ii)

Marks (more than)	No. of students
0	60
10	53
20	42
30	33
40	8