Question

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

Answer 1

70

Explanation:

The mean of the reciprocals of the terms in the two groups are `1/75` and `1/65`, respectively.

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

The sum of the reciprocals of all 28 elements is `1/5+1/5 = 2/5`.

Hence their mean is `2/5 div 28 = 1/70`

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