Question

The A.M., G.M. and H.M. in any series are equal then

• A. the distribution is symmetric
• B. all the values are same
• C. the distribution is unimodal
• D. None of these

Answer 1

The correct option is B all the values are same

Let us assume the series is $a,a,a,...$
A.M.$=\frac{a+a+a+...\text{upto}n\text{terms}}{n}=\frac{an}{n}=a$
G.M.$=\sqrt[n]{na.a.a...\text{upto}n\text{terms}}=a^n\cdot {}^{\frac{1}{n}}=a$
H.M$=\frac{2a^2}{a+a}=a$
Thus, A.M., G.M. and H.M. in any series are equal then all
the values are same.