The reciprocal of the mean of the reciprocals | vedclass

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Question

(C) Let the $n$ observations be $x_1, x_2, \dots, x_n$.The reciprocals of these observations are $\frac{1}{x_1}, \frac{1}{x_2}, \dots, \frac{1}{x_n}$.

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$H.M.$

Vedclass · Answer

(C) Let the $n$ observations be $x_1, x_2, \dots, x_n$.The reciprocals of these observations are $\frac{1}{x_1}, \frac{1}{x_2}, \dots, \frac{1}{x_n}$.The mean of these reciprocals is $\frac{\frac{1}{x_1} + \frac{1}{x_2} + \dots + \frac{1}{x_n}}{n}$.The reciprocal of this mean is $\frac{n}{\frac{1}{x_1} + \frac{1}{x_2} + \dots + \frac{1}{x_n}}$.This expression is the definition of the Harmonic Mean $(H.M.)$ of the $n$ observations.

$x_i$	$5$	$15$	$25$	$35$	$45$	$55$
$f_i$	$12$	$18$	$27$	$20$	$17$	$6$

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

The reciprocal of the mean of the reciprocals of $n$ observations is their

Similar Questions

Find the mean of the following frequency distribution:

$x_i$ $5$ $15$ $25$ $35$ $45$ $55$

$f_i$ $12$ $18$ $27$ $20$ $17$ $6$

Which of the following,in the case of discrete data,is not equal to the median?

The median of a set of $19$ observations is $30$. If two observations with values $8$ and $32$ are added,what is the median of the new set of $21$ observations?

The arithmetic mean of a set of observations is $\overline{X}$. If each observation is divided by $\alpha$ and then increased by $10$,then the mean of the new series is

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

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