In a data,if the number i is repeated i times | vedclass

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(C) Given that the number $i$ is repeated $i$ times for $i = 1, 2, \ldots, n$. The sum of the observations is $\sum_{i=1}^{n} i 	imes i = \sum_{i=1}^

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$\frac{2n+1}{3}$

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(C) Given that the number $i$ is repeated $i$ times for $i = 1, 2, \ldots, n$. The sum of the observations is $\sum_{i=1}^{n} i 	imes i = \sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}$. The total number of observations is $\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$. The mean $\bar{X}$ is given by the ratio of the sum of observations to the total number of observations: $\bar{X} = \frac{\sum i^2}{\sum i} = \frac{\frac{n(n+1)(2n+1)}{6}}{\frac{n(n+1)}{2}} = \frac{2n+1}{3}$.

Marks obtained	No. of students
$0-10$	$2$
$10-20$	$18$
$20-30$	$30$
$30-40$	$45$
$40-50$	$35$
$50-60$	$20$
$60-70$	$6$
$70-80$	$3$

In a data,if the number $i$ is repeated $i$ times for $i=1, 2, \ldots, n$,then the mean of the data is

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Marks obtained No. of students

$0-10$ $2$

$10-20$ $18$

$20-30$ $30$

$30-40$ $45$

$40-50$ $35$

$50-60$ $20$

$60-70$ $6$

$70-80$ $3$

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