The coefficient of variation and standard dev | vedclass

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(B) Given,Coefficient of Variation $(CV) = 60$ and Standard Deviation $(\sigma) = 21$. We know that $CV = \frac{\sigma}{\mu} 	imes 100$,where $\mu$ i

Vedclass · Accepted Answer

$42$

Vedclass · Answer

(B) Given,Coefficient of Variation $(CV) = 60$ and Standard Deviation $(\sigma) = 21$. We know that $CV = \frac{\sigma}{\mu} 	imes 100$,where $\mu$ is the mean. Substituting the values: $60 = \frac{21}{\mu} 	imes 100 \Rightarrow \mu = \frac{2100}{60} = 35$. When a constant $k = 15$ is added to every observation,the standard deviation remains unchanged,so $\sigma' = \sigma = 21$. The new mean becomes $\mu' = \mu + 15 = 35 + 15 = 50$. The new coefficient of variation is $CV' = \frac{\sigma'}{\mu'} 	imes 100$. $CV' = \frac{21}{50} 	imes 100 = 21 	imes 2 = 42$. Thus,the correct option is $B$.

$x_{i}$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$f_{i}$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$

$X$	$c$	$2c$	$3c$	$4c$	$5c$	$6c$
$f$	$2$	$1$	$1$	$1$	$1$	$1$

The coefficient of variation and standard deviation of an ungrouped data are $60$ and $21$ respectively. If $15$ is added to every observation of the data,then the coefficient of variation of the new data is

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