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

1 Answer
Ananda Dasgupta
Jun 8, 2018

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.

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