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Harmonic Mean Formula

Harmonic Mean is also one of the different kinds of average and it is applied for the situations when you have desired rates of average.

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.
x1, x2, x3, .... xn = Individual terms or individual values.

 Related Calculators Harmonic Mean Calculator Calculator Mean absolute mean deviation calculator Arithmetic Mean Calculator

Harmonic Mean Problems

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

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