Question

How harmonic mean is different from arithmetic mean?

Answer 1

Harmonic and Arithmetic mean:

A harmonic progression is a series of the reciprocals of its terms in arithmetic progression, and the harmonic mean (or simply HM) may be computed by dividing the number of terms by their reciprocals.

Therefore,

1. $AM$, $GM$, and $HM$ are the three acknowledged Pythagorean means in mathematics. That is, the arithmetic mean, the geometric mean, and the harmonic mean.
2. The arithmetic mean is computed by summing all of the numbers and dividing the total number of observations in the data-set by the total number of observations.
3. If $a$, $b$, and $c$ are data set observations, then the arithmetic mean = $\frac{(a+b+c)}{3}.$
4. Harmonic mean is used to calculate average units such as speed, rates, and ratios.
5. If $x$, $y$, and $z$ are three observations from a data set, the harmonic mean is: $HM=\frac{3}{\left[\left({\displaystyle \frac{1}{x}}\right)+\left({\displaystyle \frac{1}{y}}\right)+\left({\displaystyle \frac{1}{z}}\right)\right]}$.
6. If $a$, $b$, $c$, and $d$ are the harmonic progression numbers, then $\frac{1}{a}$, $\frac{1}{b}$, $\frac{1}{c}$, and $\frac{1}{d}$ will be in AP.

Hence, this is how the harmonic mean is different from the arithmetic mean.