The variance of the first ten multiples of 3 | vedclass

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(D) The first ten multiples of $3$ are $3, 6, 9, 12, 15, 18, 21, 24, 27, 30$.This is an arithmetic progression with $n = 10$ terms,where the first ter

Vedclass · Accepted Answer

$74.25$

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(D) The first ten multiples of $3$ are $3, 6, 9, 12, 15, 18, 21, 24, 27, 30$.This is an arithmetic progression with $n = 10$ terms,where the first term $a = 3$ and common difference $d = 3$.The variance of the first $n$ terms of an arithmetic progression with common difference $d$ is given by the formula $\sigma^2 = \frac{(n^2 - 1)d^2}{12}$.Substituting the values $n = 10$ and $d = 3$:$\sigma^2 = \frac{(10^2 - 1) 	imes 3^2}{12}$$\sigma^2 = \frac{(100 - 1) 	imes 9}{12}$$\sigma^2 = \frac{99 	imes 9}{12} = \frac{891}{12} = 74.25$.Thus,the variance is $74.25$.

$X_i$	$0$	$1$	$2$	$3$	$4$	$5$
$f_i$	$k+2$	$2k$	$k^2-1$	$k^2-1$	$k^2-1$	$k-3$

$x_i$	$6$	$10$	$14$	$18$	$24$	$28$	$30$
$f_i$	$2$	$4$	$7$	$12$	$8$	$4$	$3$

The variance of the first ten multiples of $3$ is

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