If the variance of the following data :

$6, 8, 10, 12, 14, 16, 18, 20, 22, 24$ is $K$ , then the value of $\frac{K}{11}$ is

Question

If the variance of the following data : 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 is K , then the value of K 11 is,

MARKS App · Accepted Answer

The given data is : 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 ∴ x ¯ = 6 + 8 + 1 0 + 1 2 + 1 4 + 1 6 + 1 8 + 2 0 + 2 2 + 2 4 1 0 = 1 5 0 1 0 = 1 5 The table is as below : x i x i - x ¯ x i - x ¯ 2 6 - 9 81 8 - 7 49 10 - 5 25 12 - 3 9 14 - 1 1 16 1 1 18 3 9 20 5 25 22 7 49 24 9 81 Total 330 Hence, Variance σ 2 = Σ x i - x ¯ 2 n = 3 3 0 1 0 = 3 3 . ​

$x_{i}$	$x_{i} - \bar{x}$	${(x_{i} - \bar{x})}^{2}$
$6$	$- 9$	$81$
$8$	$- 7$	$49$
$10$	$- 5$	$25$
$12$	$- 3$	$9$
$14$	$- 1$	$1$
$16$	$1$	$1$
$18$	$3$	$9$
$20$	$5$	$25$
$22$	$7$	$49$
$24$	$9$	$81$
$Total$		$330$

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