The mean of a set of n numbers,when each is d | vedclass

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(B) Let the $n$ numbers be $x_1, x_2, x_3, \ldots, x_n$. The mean of these numbers is $\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$. When each number is di

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$X$

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(B) Let the $n$ numbers be $x_1, x_2, x_3, \ldots, x_n$. The mean of these numbers is $\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$. When each number is divided by $5$,the new set of numbers is $\frac{x_1}{5}, \frac{x_2}{5}, \ldots, \frac{x_n}{5}$. The mean of this new set is given as $\frac{X}{5}$. Therefore,$\frac{\frac{x_1}{5} + \frac{x_2}{5} + \ldots + \frac{x_n}{5}}{n} = \frac{X}{5}$. $\frac{1}{5} \left( \frac{\sum_{i=1}^{n} x_i}{n} \right) = \frac{X}{5}$. Multiplying both sides by $5$,we get $\frac{\sum_{i=1}^{n} x_i}{n} = X$. Thus,the mean of the original $n$ numbers is $X$.

Class	$0-4$	$4-8$	$8-12$	$12-16$	$16-20$
Frequency	$3$	$9$	$10$	$8$	$6$

The mean of a set of $n$ numbers,when each is divided by $5$,is $\frac{X}{5}$. What is the mean of the original $n$ numbers?

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