The mean of a set of numbers is bar{x}. If ea | vedclass

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(C) Let the set of numbers be $x_1, x_2, \dots, x_n$. The mean is given by $\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$,which implies $\sum_{i=1}^{n} x_i

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$\lambda \bar{x}$

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(C) Let the set of numbers be $x_1, x_2, \dots, x_n$. The mean is given by $\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$,which implies $\sum_{i=1}^{n} x_i = n\bar{x}$.If each number is multiplied by $\lambda$,the new set of numbers is $\lambda x_1, \lambda x_2, \dots, \lambda x_n$.The new mean is $\frac{\sum_{i=1}^{n} \lambda x_i}{n} = \frac{\lambda \sum_{i=1}^{n} x_i}{n}$.Substituting $\sum x_i = n\bar{x}$,we get the new mean as $\frac{\lambda (n\bar{x})}{n} = \lambda \bar{x}$.

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

Size of Item	$1$	$2$	$3$	$4$	$5$	$6$	$7$
Frequency	$2$	$4$	$5$	$8$	$7$	$3$	$2$

The mean of a set of numbers is $\bar{x}$. If each number is multiplied by $\lambda$,then the mean of the new set is

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