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 $5$.

Heights (in $cm$)	Number of students
$150-153$	$7$
$153-156$	$8$
$156-159$	$14$
$159-162$	$10$
$162-165$	$6$
$165-168$	$5$

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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Heights (in $cm$) Number of students

$150-153$ $7$

$153-156$ $8$

$156-159$ $14$

$159-162$ $10$

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$165-168$ $5$

The information regarding the marks scored by $30$ students in a $50$ marks test is given below:

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Number of students $(f_{i})$ $2$ $3$ $5$ $6$ $6$ $4$ $3$ $1$

Find the mean of the data.

The mean of natural numbers between $1$ to $20$ which are multiples of $3$ is ..........

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