# What is the harmonic mean?

##### 1 Answer
May 17, 2018

The harmonic mean is a type of average represented by the following formula.

$H = \frac{n}{\frac{1}{x} _ 1 + \frac{1}{x} ^ 2. . . + \frac{1}{x} _ n}$.

#### Explanation:

The harmonic mean is a specific type of average used when calculating averages of units or rates, such as speed speed. It is different than the arithmetic mean and is always lower.

The formula is:

$H = \frac{n}{\frac{1}{x} _ 1 + \frac{1}{x} ^ 2. . . + \frac{1}{x} _ n}$

$n$ represents the number of terms in the data set. ${x}_{1}$ represents the first value in the set.

For example, take the following problem.

What is the harmonic mean of 2,4,5,8,10?

$H = \frac{5}{\frac{1}{2} + \frac{1}{4} + \frac{1}{5} + \frac{1}{8} + \frac{1}{10}}$

$H = \frac{5}{1.175}$

$H = 4.255$