If the mean of a data bar{x} is 10 and if all | vedclass

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(D) Let the observations be $x_1, x_2, x_3, \ldots, x_n$. The mean is given by $\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n} = 10$. When each observation is

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$20$

Vedclass · Answer

(D) Let the observations be $x_1, x_2, x_3, \ldots, x_n$. The mean is given by $\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n} = 10$. When each observation is multiplied by $2$,the new observations become $2x_1, 2x_2, 2x_3, \ldots, 2x_n$. The new mean $\bar{x}_{new} = \frac{\sum_{i=1}^{n} (2x_i)}{n} = 2 	imes \left( \frac{\sum_{i=1}^{n} x_i}{n} ight)$. Substituting the value of the original mean,we get $\bar{x}_{new} = 2 	imes 10 = 20$.

Height (in $cm$)	$160$	$150$	$152$	$161$	$156$	$154$	$155$
No of students	$12$	$8$	$4$	$4$	$3$	$3$	$7$

$x_i$	$3$	$6$	$9$	$12$
$f_i$	$1$	$2$	$3$	$4$

If the mean of a data $\bar{x}$ is $10$ and if all the observations are multiplied by $2$,then the mean of the new data is

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