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

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(D) The mean is calculated using the formula $	ext{Mean} = \frac{\sum x_i f_i}{\sum f_i}$.Given values $x_i = \{1, \frac{1}{2}, \frac{1}{3}, \dots, \

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) The mean is calculated using the formula $	ext{Mean} = \frac{\sum x_i f_i}{\sum f_i}$.Given values $x_i = \{1, \frac{1}{2}, \frac{1}{3}, \dots, \frac{1}{n}\}$ and frequencies $f_i = \{1, 2, 3, \dots, n\}$.Sum of products $\sum x_i f_i = (1 	imes 1) + (\frac{1}{2} 	imes 2) + (\frac{1}{3} 	imes 3) + \dots + (\frac{1}{n} 	imes n) = 1 + 1 + 1 + \dots + 1$ ($n$ times) $= n$.Sum of frequencies $\sum f_i = 1 + 2 + 3 + \dots + n = \frac{n(n + 1)}{2}$.Therefore,$	ext{Mean} = \frac{n}{\frac{n(n + 1)}{2}} = \frac{2n}{n(n + 1)} = \frac{2}{n + 1}$.

Class	Frequency
$10-20$	$180$
$20-30$	$82$
$30-40$	$34$
$40-50$	$180$
$50-60$	$136$
$60-70$	$23$
$70-80$	$50$

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

Marks	$2$	$3$	$5$	$7$
Frequency	$(x+1)^2$	$2x-5$	$x^2-3x$	$x$

If the values $1, \frac{1}{2}, \frac{1}{3}, \dots, \frac{1}{n}$ have frequencies $1, 2, 3, \dots, n$ respectively,what is their mean?

Similar Questions

Find the median for the following distribution:
Class Frequency
$10-20$ $180$
$20-30$ $82$
$30-40$ $34$
$40-50$ $180$
$50-60$ $136$
$60-70$ $23$
$70-80$ $50$

Let $M$ denote the median of the following frequency distribution. Then $20M$ is equal to:

Class $0-4$ $4-8$ $8-12$ $12-16$ $16-20$

Frequency $3$ $9$ $10$ $8$ $6$

If for some positive $x \in R$,the frequency distribution of the marks obtained by $20$ students in a certain test is as follows:
Marks $2$ $3$ $5$ $7$
Frequency $(x+1)^2$ $2x-5$ $x^2-3x$ $x$

Then the mean of the marks is:

$A$ student scores $75\%, 80\%,$ and $85\%$ in three subjects. If the marks of a fourth subject are added,what is the minimum possible average percentage?

What is the weighted mean of the first $n$ natural numbers if the weights are equal?

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