NCERT Class 10 Mathematics

STATISTICS 261

x =^1

1

n

ii

i

n

i

i

fx

f

✁

✁

which, more briefly, is written as x =

✂

✂

ii

i

fx

f

, if it is understood that i varies from

1 to n.

Let us apply this formula to find the mean in the following example.

Example 1 : The marks obtained by 30 students of Class X of a certain school in a
Mathematics paper consisting of 100 marks are presented in table below. Find the
mean of the marks obtained by the students.

Marks obtained 10 20 36 40 50 56 60 70 72 80 88 92 95

(xi)

Number of 1134324411231

student (fi)

Solution: Recall that to find the mean marks, we require the product of each xi with
the corresponding frequency fi. So, let us put them in a column as shown in Table 14.1.

Table 14.1

Marks obtained (xi) Number of students (fi) fixi

10 1 10

20 1 20

36 3 108

40 4 160

50 3 150

56 2 112

60 4 240

70 4 280

72 1 72

80 1 80

88 2 176

92 3 276

95 1 95

Total ✄fi = 30 ✄fixi = 1779