Question

If the variance of the frequency distribution

xi	Frequency ft
2	3
3	6
4	16
5	\(\alpha\)
6	9
7	5
8	6

is 3 , then $\alpha$ is equal to

Hint:

To find the variance of a frequency distribution, first calculate \( d_i \) for each \( x_i \), then use the formula for variance \( \sigma^2 = \frac{\sum f_i d_i^2}{\sum f_i} - \left( \frac{\sum f_i d_i}{\sum f_i} \right)^2 \) to determine the result.

Answer 1

Correct Answer: 0

The correct answer is 5.

xi	fi	di=xi-5	fidi2	ffdf
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

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