Find the coefficient of variation of the firs | vedclass

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Question

(A) For the first $n$ natural numbers,the mean $\bar{x} = \frac{n+1}{2}$.The standard deviation $\sigma = \sqrt{\frac{n^2-1}{12}}$.The coefficient of

Vedclass · Accepted Answer

$\sqrt{\frac{n-1}{3(n+1)}} 	imes 100$

Vedclass · Answer

(A) For the first $n$ natural numbers,the mean $\bar{x} = \frac{n+1}{2}$.The standard deviation $\sigma = \sqrt{\frac{n^2-1}{12}}$.The coefficient of variation ($C$.$V$.) is given by $\frac{\sigma}{\bar{x}} 	imes 100$.Substituting the values: $C.V. = \sqrt{\frac{n^2-1}{12}} 	imes \frac{2}{n+1} 	imes 100$.Since $n^2-1 = (n-1)(n+1)$,we have $C.V. = \sqrt{\frac{(n-1)(n+1)}{12}} 	imes \frac{2}{n+1} 	imes 100$.$C.V. = \sqrt{\frac{(n-1)(n+1)}{3 	imes 4}} 	imes \frac{2}{n+1} 	imes 100 = \sqrt{\frac{n-1}{3(n+1)}} 	imes \frac{\sqrt{n+1}}{2} 	imes \frac{2}{n+1} 	imes 100$.Simplifying,we get $C.V. = \sqrt{\frac{n-1}{3(n+1)}} 	imes 100$.

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

Find the coefficient of variation of the first $n$ natural numbers.

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