If the values 1, frac{1}{2}, frac{1}{3}, frac | vedclass

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(D) The mean $\bar{x}$ is given by the formula $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$.Here,the values $x_i$ are $1, \frac{1}{2}, \frac{1}{3}, \dots

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

Vedclass · Answer

(D) The mean $\bar{x}$ is given by the formula $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$.Here,the values $x_i$ are $1, \frac{1}{2}, \frac{1}{3}, \dots, \frac{1}{n}$ and their corresponding frequencies $f_i$ are $1, 2, 3, \dots, n$.Sum of products $\sum f_i x_i = (1 	imes 1) + (2 	imes \frac{1}{2}) + (3 	imes \frac{1}{3}) + \dots + (n 	imes \frac{1}{n}) = 1 + 1 + 1 + \dots + 1$ ($n$ times) $= n$.Sum of frequencies $\sum f_i = 1 + 2 + 3 + \dots + n = \frac{n(n+1)}{2}$.Therefore,the mean $\bar{x} = \frac{n}{\frac{n(n+1)}{2}} = \frac{2n}{n(n+1)} = \frac{2}{n+1}$.

Height (in $cm$)	$160$	$150$	$152$	$161$	$156$	$154$	$155$
No of students	$12$	$8$	$4$	$4$	$3$	$3$	$7$

If the values $1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \dots, \frac{1}{n}$ occur at frequencies $1, 2, 3, 4, 5, \dots, n$ in a distribution,then the mean is

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