Question

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

Answer 1

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.