Harmonic mean

Harmonic means are a type of mean. It is the number of values divided by the reciprocal of the values. If there are <math>N</math> numbers <math>X_1,X_2,X_3...X_N</math>, then the harmonic mean of these numbers are <math display="block"> \frac{N}{\frac{1}{X_1}+\frac{1}{X_2}+\frac{1}{X_3}+\dots + \frac{1}{X_N}}</math>

Out of the geometric mean and arithmetic mean, the harmonic mean is usually the smallest.

Example

Let's find the harmonic mean of 2,4 and 5. There are three numbers so we will be dividing three. The reciprocals of the numbers are <math>\frac{1}{2}</math>, <math>\frac{1}{4}</math> and <math>\frac{1}{5}</math>. If we add the reciprocals we get <math>\frac{19}{20}</math>. If we divide three by this number, the result is <math>\frac{60}{19}</math> (approximately 3.157894737)