If each observation of the data is increased | vedclass

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(A) Let the observations be $x_1, x_2, ..., x_n$. The mean is $\bar{x} = \frac{\sum x_i}{n}$.If each observation is increased by $5$,the new observati

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is increased by $5$

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(A) Let the observations be $x_1, x_2, ..., x_n$. The mean is $\bar{x} = \frac{\sum x_i}{n}$.If each observation is increased by $5$,the new observations are $(x_1+5), (x_2+5), ..., (x_n+5)$.The new mean $\bar{x}' = \frac{\sum (x_i+5)}{n} = \frac{\sum x_i + 5n}{n} = \frac{\sum x_i}{n} + \frac{5n}{n} = \bar{x} + 5$.Therefore,if each observation of the data is increased by $5$,then their mean is also increased by $5$.

Marks $(x_{i})$	$15$	$22$	$28$	$31$	$35$	$40$	$44$	$46$
Number of students $(f_{i})$	$2$	$3$	$5$	$6$	$6$	$4$	$3$	$1$

If each observation of the data is increased by $5,$ then their mean

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