The reciprocal of the arithmetic mean of the reciprocal is called as **Harmonic Mean.** It is calculated by dividing the number of observations by the sum of reciprocal of the observation.

The formula to find the harmonic mean is given by:

Where, n = Total number of numbers or terms.

x_{1}, x_{2}, x_{3}, .... x_{n} = Individual terms or individual values.

x

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Harmonic Mean Calculator | Calculator Mean |

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Below are the solved problems based on harmonic mean : ### Solved Examples

**Question 1: **Find the harmonic mean of the following data {8, 9, 6, 11, 10, 5} ?

** Solution: **

Given data: {8, 9, 6, 11, 10, 5}

So Harmonic mean = $\frac{6}{\frac{1}{8}+\frac{1}{9}+\frac{1}{6}+\frac{1}{11}+\frac{1}{10}+\frac{1}{5}}$

H = $\frac{6}{0.7936}$ = 7.560

Harmonic mean(H) = 7.560

**Question 2: **Find the harmonic mean of the following data {90, 35, 45, 76, 58, 37, 87} ?

** Solution: **

Given data:{90, 35, 45, 76, 58, 37, 87}

Harmonic mean(H) = $\frac{7}{\frac{1}{90}+\frac{1}{35}+\frac{1}{45}+\frac{1}{76}+\frac{1}{58}+\frac{1}{37}+\frac{1}{87}}$

= $\frac{7}{0.1308}$ = 53.5168

Harmonic mean(H) = 53.5168

Given data: {8, 9, 6, 11, 10, 5}

So Harmonic mean = $\frac{6}{\frac{1}{8}+\frac{1}{9}+\frac{1}{6}+\frac{1}{11}+\frac{1}{10}+\frac{1}{5}}$

H = $\frac{6}{0.7936}$ = 7.560

Harmonic mean(H) = 7.560

Given data:{90, 35, 45, 76, 58, 37, 87}

Harmonic mean(H) = $\frac{7}{\frac{1}{90}+\frac{1}{35}+\frac{1}{45}+\frac{1}{76}+\frac{1}{58}+\frac{1}{37}+\frac{1}{87}}$

= $\frac{7}{0.1308}$ = 53.5168

Harmonic mean(H) = 53.5168