Question

Is harmonic mean greater than arithmetic mean?

Answer 1

Determine if the harmonic mean is greater than the arithmetic mean

The arithmetic mean is the average of a given set of data. It can be represented as:

$A.M=\frac{x_1+x_2+x_3}{3}$

Where $x_1,x_2,x_3\text{are in}A.P\text{and}\text{'}n\text{'}\text{is the number of observations}=3.$

While the harmonic mean is the reciprocal of the arithmetic mean. It can be represented as:

$$\begin{gathered} H.M=\frac{1}{A.M} \\ \Rightarrow H.M=\frac{n}{{\displaystyle \frac{1}{x_1}}+{\displaystyle \frac{1}{x_2}}+{\displaystyle \frac{1}{x_3}}} \\ \therefore H.M<A.M \end{gathered}$$

Hence, the harmonic mean is less than the arithmetic mean.