## Definition

In mathematics, the harmonic mean is one of several kinds of average, and in particular one of the Pythagorean means. Typically, it is appropriate for situations when the average of rates is desired.

### What is 'Harmonic Average'

The mean of a set of positive variables. Calculated by dividing the number of observations by the reciprocal of each number in the series.

Also known as "harmonic mean".

### Explaining 'Harmonic Average'

Alternately, the harmonic average could be thought of as the reciprocal of the arithmetic mean of inverse values.

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Yes, it could be thought as reciprocal arithmetic mean inverse values.

#### What is the harmonic mean?

The harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means.

#### How do you calculate the harmonic average?

You divide the number of observations by the reciprocal each number in the series.

#### How can you express it as a reciprocal?

You can express it as the reciprocal of the arithmetic mean of reciprocals. As a simple example, the harmonic mean of 1, 4, and 4 is .

#### What does it typically refer to?

It typically refers to situations when the average of rates is desired.

#### What is another name for this type of average?

It could also be thought as "harmonic mean".

#### What is the mean of a set of positive variables?

The mean of a set of positive variables is called the harmonic average.