Maths

STATISTICS 261
x =
n
✁ fx
i 1
n
i 1
i
✁ f
i
i
fixi
which, more briefly, is written as x = , if it is understood that i varies from
✂ f ✂
i
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
(x i
)
Number of 1 1 3 4 3 2 4 4 1 1 2 3 1
student ( f i
)
Solution: Recall that to find the mean marks, we require the product of each x i
with
the corresponding frequency f i
. So, let us put them in a column as shown in Table 14.1.
Table 14.1
Marks obtained (x i
) Number of students ( f i
) f i
x i
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 ✄f i
= 30 ✄f i
x i
= 1779