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Q. The reciprocal of the mean of the reciprocals of $n$ observation is the :

Statistics

Solution:

Let $x_{1}, x_{2}, \ldots \ldots \ldots . . x_{n}$ be $n$ observation.
Now, reciprocals of $n$ observations are
$\frac{1}{ x _{1}}, \frac{1}{ x _{2}}, \ldots \ldots, \frac{1}{ x _{ n }}$
Now, mean of the reciprocals of $n$ observation.
$=\frac{1}{ x _{1}}+\frac{1}{ x _{2}}+\ldots \ldots+\frac{1}{ x _{ n }}$
Now, reciprocal of mean of the reciprocals of $n$ observations
$=\frac{ n }{\frac{1}{ x _{1}}+\frac{1}{ x _{2}}+\ldots \ldots .+\frac{1}{ x _{ n }}}=$ Harmonic mean