If the AM and GM for 10 observations are both 15 then the value of harmonic mean......?

1 Answer
Ananda Dasgupta
Jun 8, 2018

15 (Assuming all the observations are nonnegative)

Explanation:

The generalized AM-GM theorem says that if #a_1,a_2,...,a_n# are non-negative, then

#(a_1+a_2+...+a_n)/n >= root{n}{a_1a_2...a_n}#

with equality holding only when

#a_1 = a_2 = ... = a_n#

Thus, in this case, all the observations (assumed non-negative) must be 15, and their harmonic mean must be the same.

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