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(C) We know that for a random variable $X$,the variance of $aX$ is given by $\operatorname{Var}(aX) = a^2 \cdot \operatorname{Var}(X)$.Given that the

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$|\lambda| \sigma$

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(C) We know that for a random variable $X$,the variance of $aX$ is given by $\operatorname{Var}(aX) = a^2 \cdot \operatorname{Var}(X)$.Given that the original variance is $\sigma^2$,the variance of the new observations (where each observation is multiplied by $\lambda$) is $\operatorname{Var}(\lambda X) = \lambda^2 \cdot \operatorname{Var}(X) = \lambda^2 \sigma^2$.The standard deviation is the square root of the variance.Therefore,the new standard deviation is $\sqrt{\lambda^2 \sigma^2} = |\lambda| \sigma$.

\text{Parameter}	\text{Plant } $A$ \text{ and } $B$ \text{ Data}
\text{No. of workers}	$A: 500, B: 6000$
\text{Average monthly wages}	$A: Rs. 2500, B: Rs. 2500$
\text{Variance of distribution of wages}	$A: 81, B: 100$

Class	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
$f_i$	$3$	$7$	$12$	$15$	$8$	$3$	$2$

If each observation of a distribution with variance $\sigma^2$ is multiplied by $\lambda$,find the standard deviation of the new observations.

Similar Questions

Calculate the mean,variance,and standard deviation for the following distribution:

Class $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$

$f_i$ $3$ $7$ $12$ $15$ $8$ $3$ $2$

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