If there are two groups with 75 and 65 as harmonic mean and containing 15 and 13 observations then the combined harmonic mean....?
The mean of the reciprocals of the terms in the two groups are
Thus, the sum of the reciprocals of the terms in the first group is
and that of the second group is also
The sum of the reciprocals of all 28 elements is
Hence their mean is
So, the harmonic mean of all the numbers together is 70.