The mean of a set of 30 observations is 75. I | vedclass

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(B) Let the observations be $x_1, x_2, \dots, x_{30}$. The mean is given by $\bar{x} = \frac{1}{30} \sum_{i=1}^{30} x_i = 75$.When each observation is

Vedclass · Accepted Answer

$\frac{4}{3}$

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(B) Let the observations be $x_1, x_2, \dots, x_{30}$. The mean is given by $\bar{x} = \frac{1}{30} \sum_{i=1}^{30} x_i = 75$.When each observation is multiplied by $\lambda$ and decreased by $25$,the new observations are $y_i = \lambda x_i - 25$.The new mean is $\bar{y} = \frac{1}{30} \sum_{i=1}^{30} (\lambda x_i - 25) = \lambda \left( \frac{1}{30} \sum_{i=1}^{30} x_i \right) - 25 = 75\lambda - 25$.According to the problem,the mean remains the same,so $\bar{y} = 75$.Thus,$75\lambda - 25 = 75$.$75\lambda = 100$.$\lambda = \frac{100}{75} = \frac{4}{3}$.

$Country$	$Agriculture$	$Industries$	$Services$	$Others$
$India$	$45$	$19$	$28$	$4$
$U.K.$	$3$	$40$	$44$	$13$
$Japan$	$6$	$48$	$43$	$3$
$U.S.A.$	$3$	$35$	$61$	$1$

The mean of a set of $30$ observations is $75$. If each observation is multiplied by a non-zero number $\lambda$ and then each of them is decreased by $25$,their mean remains the same. The value of $\lambda$ is equal to

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