Question

Obtain the mean of the given data by assumed mean method. $x_i$ $f_i$

25	3
35	5
45	4
55	6
65	8
75	10
85	9

• A. 66.11
• B. 55.22
• C. 50.14
• D. 62.14

Answer 1

The correct option is A 66.11

Suppose we assume ‘ A = 55’ as assumed mean, then deviation of other observations from the assumed mean is given in table.

Sum of frequencies = 18
$\sum f_i$ = 18

Sum of the $f_i\times d_i$ products = (-90) + (-100) + (-40) + 0 + 80 + 200 + 270 = 200 $x_i$ $f_i$ $d_i=x-A$ $f_i{d}_i$

25	3	-30	-90
35	5	-20	-100
45	4	-10	-40
A=55	6	0	0
65	8	10	80
75	10	20	200
85	9	30	270
	$\sum f_i$ = 18		$\sum f_i{d}_i$ = 200

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

$=55+\frac{200}{18}$

$=55+11.11=66.11$

Thus, the mean for the given data is 66.11.