Question

The variance of the following data is

$x_i$	1	2	3	4	5	6	7	8	9	10
$f_i$	1	2	3	4	5	6	7	8	9	10

• A. 10
• B. 9
• C. 8
• D. 6

Answer 1

Answer: (D)

According to given data ,

$\bar{x}-x_i$

$x_i$	$f_i$	$x_i{f}_i$	$f_i{\left(\bar{x}-x_i\right)}^2$
1	1	1	6	36
2	2	4	5	50
3	3	9	4	48
4	4	16	3	36
5	5	25	2	20
6	6	36	1	6
7	7	49	0	0
8	8	64	1	8
9	9	81	2	36
10	10	100	3	90

$\because N=\Sigma f_i=55,\bar{x}=\frac{\Sigma x_i{f}_i}{N}$
$=\frac{10\times 11\times 21}{6\times 55}=7$
$\therefore {\sigma }^2=\frac{\Sigma f_i{\left(\bar{x}-x_i\right)}^2}{N}$
$=\frac{36+50+48+36+20+6+8+36+90}{55}$
$=\frac{330}{55}=6$