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

Jun 8, 2018

70

#### Explanation:

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

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

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

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

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