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Harmonic Mean Calculator

To calculate the harmonic mean of the data set with steps, input the data set and hit the calculate button using this harmonic mean calculator.

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Harmonic mean calculator is an online tool used to compute the harmonic mean of the given data set x. This harmonic average calculator uses both positive and negative integers as an input to calculate the H.M with steps.

How to use this harmonic mean calculator?

Follow the below steps to calculate the harmonic mean of the given data set.

  • Enter the comma-separated values.
  • Press the calculate button
  • Click the show more button to view the steps.
  • Use the reset button to calculate another data set.

What is the harmonic mean?

The harmonic mean is a type of numerical mean. It is evaluated by dividing the total number of observations by the reciprocal of each number in the given set of data. In simple words, the harmonic mean is the reciprocal of the arithmetic mean’s reciprocals.

The general equation of the harmonic mean is:

Harmonic mean formula

  • H.M is the harmonic mean.
  • n is the total number of observations.
  • (x1, x2, x3,..., xn) are the terms of the given data set.

The other types of the numerical mean are geometric mean and arithmetic mean.

How to calculate the harmonic mean?

Following is a solved example of the harmonic mean.

Example

Find the harmonic mean of 21, 43, 12, 11, 39, and 8.

Solution

Step 1: Write the given data set in ascending order.

8, 11, 12, 21, 39, 43

Step 2: Write the general formula of the harmonic mean.

Harmonic mean formula 1

Step 3: Put the values of the given dataset in the formula.

harmonic mean calculation

Step 4: Convert the fractions into decimals.

harmonic mean calculation
harmonic mean calculation
H.M = 15.161

FAQs

what is the harmonic mean of 5 and 2?

Answer: The harmonic mean of 5 and 2 is 2.8571

What is the harmonic mean of 12 and 6?

Answer: The harmonic mean of 12 and 6 is 8

What is the harmonic mean of 1/2 and 3?

Answer: The harmonic mean of 1/2 and 3 is 0.8571

What is the harmonic mean for the numbers 2 3 5?

Answer: The harmonic mean of 2, 3, and 5 is 2.9032
 

References

  1. Hayes, A. (2022, February 8). What is the harmonic mean?. Investopedia.
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