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.

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

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