Question

The following data give the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students by assumed mean method.
Age (in years) Number of students

13	3
14	8
15	9
16	11
17	6
18	3

• A. 17.25
• B. 15.45
• C. 16.55
• D. 18.35

Answer 1

The correct option is B 15.45

Suppose we assume ‘16’ as a mean, then the deviation of other observations from the assumed mean is given in table.

Sum of frequencies = 40
$\sum f_i$ = 40

Sum of the $f_i\times d_i$ products = (-9) + (-16) + (-9) + 0 + 6 + 6 = -22
$\sum f_i{d}_i$ = -22
$x_i$ $f_i$ $d=x-A$ $f_i{d}_i$

13	3	-3	-9
14	8	-2	-16
15	9	-1	-9
16=A	11	0	0
17	6	1	6
18	3	2	6
	$\sum f_i$ = 40		$\sum f_i{d}_i$ = -22

$Mean=A+\frac{\sum f_i{d}_i}{\sum f_i}$

$=16+\frac{(-22)}{40}$

$=16-\frac{22}{40}$

$=16-0.55=15.45$

Hence the required arithmetic mean for the given data is 15.45