Question

If the variance of the frequency distribution

$x_i$	Frequency $f_t$
2	3
3	6
4	16
5	$\alpha$
6	9
7	5
8	6

is 3 , then $\alpha$ is equal to

Answer 1

Answer: 5

$x_i$	$f_i$	$d_i=x_i-5$	$f_i{d}_i^2$	$f_i{d}_i$
2	3	-3	27	-9
3	6	-2	24	-12
4	16	-1	16	-16
5	$\alpha$	0	0	0
6	9	1	9	9
7	5	2	20	10
8	6	3	54	18

${\sigma }_x^2={\sigma }_d^2=\frac{\sum f_i{d}_i{}^2}{\sum f_i}-{\left(\frac{\sum f_i{d}_i}{\sum f_i}\right)}^2$
$=\frac{150}{45+\alpha }-0=3$
$\Rightarrow 150=135+3\alpha$
$\Rightarrow 3\alpha =15\Rightarrow \alpha =5$