Question

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

• A. geometric mean
• B. median
• C. harmonic mean
• D. average

Answer 1

Answer: (C)

Let $x_1,x_2,\dots \dots \dots ..x_n$ be $n$ observation.
Now, reciprocals of $n$ observations are
$\frac{1}{x_1},\frac{1}{x_2},\dots \dots ,\frac{1}{x_n}$
Now, mean of the reciprocals of $n$ observation.
$=\frac{1}{x_1}+\frac{1}{x_2}+\dots \dots +\frac{1}{x_n}$
Now, reciprocal of mean of the reciprocals of $n$ observations
$=\frac{n}{\frac{1}{x_1}+\frac{1}{x_2}+\dots \dots .+\frac{1}{x_n}}=$ Harmonic mean