If there are two groups with 75 and 65 as harmonic mean and containing 15 and 13 observations then the combined harmonic mean....?

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If there are two groups with 75 and 65 as harmonic mean and containing 15 and 13 observations then the combined harmonic mean....?

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Answer 1 · 2018-06-08T03:23:24

70

Explanation:

The mean of the reciprocals of the terms in the two groups are $\frac{1}{75}$ $1/75$ and $\frac{1}{65}$ $1/65$ , respectively.

Thus, the sum of the reciprocals of the terms in the first group is
$\frac{1}{75} \times 15 = \frac{1}{5}$ $1/75times 15 = 1/5$
and that of the second group is also
$\frac{1}{65} \times 13 = \frac{1}{5}$ $1/65 times 13 = 1/5$

The sum of the reciprocals of all 28 elements is $\frac{1}{5} + \frac{1}{5} = \frac{2}{5}$ $1/5+1/5 = 2/5$ .

Hence their mean is $\frac{2}{5} \div 28 = \frac{1}{70}$ $2/5 div 28 = 1/70$

So, the harmonic mean of all the numbers together is 70.

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If there are two groups with 75 and 65 as harmonic mean and containing 15 and 13 observations then the combined harmonic mean....?

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