The variance of the numbers 8,21,34,47, ldots | vedclass

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Question

$8+( n -1) 13=320$
$13 n =325$
$n =25$
$	ext { no. of terms }=25$
$	ext { mean }=\frac{\sum x _{ i }}{ n }=\frac{8+21+\ldots+320}{25}=\fra

Vedclass · Accepted Answer

$8788$

Vedclass · Answer

$8+( n -1) 13=320$
$13 n =325$
$n =25$
$	ext { no. of terms }=25$
$	ext { mean }=\frac{\sum x _{ i }}{ n }=\frac{8+21+\ldots+320}{25}=\frac{\frac{25}{2}(8+320)}{25}$
$	ext { variance } \sigma^2=\frac{\sum x _{ i }^2}{ n }-(	ext { mean })^2$
$=\frac{8^2+21^2+\ldots .+320^2}{13}-(164)^2$
$=8788$

${x_i}$	$3$	$8$	$13$	$18$	$25$
${f_i}$	$7$	$10$	$15$	$10$	$6$

The variance of the numbers $8,21,34,47, \ldots, 320$, is______

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