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 $\frac{\lambda (n\bar{x})}{n} = \lambda \bar{x}$.

Class	Frequency
$10-20$	$180$
$20-30$	$82$
$30-40$	$34$
$40-50$	$180$
$50-60$	$136$
$60-70$	$23$
$70-80$	$50$

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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Find the median for the following distribution:
Class Frequency
$10-20$ $180$
$20-30$ $82$
$30-40$ $34$
$40-50$ $180$
$50-60$ $136$
$60-70$ $23$
$70-80$ $50$

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