NCERT Class 10 Mathematics

STATISTICS 281

Table 14.14

Marks obtained Number of students

(Cumulative frequency)

More than or equal to 0 53

More than or equal to 10 53 – 5 = 48

More than or equal to 20 48 – 3 = 45

More than or equal to 30 45 – 4 = 41

More than or equal to 40 41 – 3 = 38

More than or equal to 50 38 – 3 = 35

More than or equal to 60 35 – 4 = 31

More than or equal to 70 31 – 7 = 24

More than or equal to 80 24 – 9 = 15

More than or equal to 90 15 – 7 = 8

The table above is called a cumulative frequency distribution of the more
than type. Here 0, 10, 20,.. ., 90 give the lower limits of the respective class intervals.

Now, to find the median of grouped data, we can make use of any of these
cumulative frequency distributions.

Let us combine Tables 14.12 and 14.13 to get Table 14.15 given below:

Table 14.15

Marks Number of students (f) Cumulative frequency (cf )

0 - 10 5 5

10 - 20 3 8

20 - 30 4 12

30 - 40 3 15

40 - 50 3 18

50 - 60 4 22

60 - 70 7 29

70 - 80 9 38

80 - 90 7 45

90 - 100 8 53

Now in a grouped data, we may not be able to find the middle observation by
looking at the cumulative frequencies as the middle observation will be some value in