The variance of the distribution given below is x 1 2 3 ..... 10 f 1 2 3 ...... 10

AP ICET 2017 Shift 1 Paper

Question : 144 of 200

Marks: +1, -0

The variance of the distribution given below is

x	1	2	3	.....	10
f	1	2	3	......	10

Solution:

$x_i$	$f_i$	$f_ix_i$	$x_i-\ov{x}=x_i=7$	$(x_i-\ov{x})^2$	$f_i(x_i-\ov{x})^2$
1	1	1	$-6$	36	36
2	2	4	$-5$	25	50
3	3	9	$-4$	16	48
4	4	16	$-3$	9	36
5	5	25	$-2$	4	20
6	6	36	$-1$	1	6
7	7	49	0	0	0
8	8	64	1	1	8
9	9	81	2	4	36
10	10	100	3	9	90
	$N=Σf_i=55$	$Σf_ix_i=385$			$Σf_i(x_i-\ov{x})^2=330$

\ov{X↖{-}}=385/55=7

Variance

=330/55=6

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