What is Harmonic Mean?

Harmonic mean is defined as the average of the reciprocal values of the given values. That is for finding the harmonic mean of the given data set we first take the reciprocal of the data set and then divide the number of the data set by the sum of the reciprocal values. The value so obtained is called the Harmonic mean.

The harmonic mean is one of the measures of the central tendency which is generally used when we have to find the rate of the data set. It is used in the statistics and financial sector to explain various parameters of the data set.

Harmonic Mean

Harmonic Mean is the type of mean that is used when we have to find the average rate of change, it is the mean calculated by taking the reciprocal values of the given value and then dividing the number of terms by the sum of the reciprocal values. The harmonic mean is one of the Pythagorean mean and the other two Pythagorean mean are,

  • Arithmetic Mean
  • Geometric Mean

These means tell us about various parameters of the data set.

Harmonic Mean also denoted as HM is the mean calculated by taking the reciprocal of the given set. In this article, we will learn about HM, its formula, examples, and others in detail.

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What is Harmonic Mean?

Harmonic mean is defined as the average of the reciprocal values of the given values. That is for finding the harmonic mean of the given data set we first take the reciprocal of the data set and then divide the number of the data set by the sum of the reciprocal values. The value so obtained is called the Harmonic mean....

Harmonic Mean Definition

Harmonic mean is one of the Pythagorean means other than Arithmetic Mean and Geometric Mean. The harmonic mean is always lower as compared to the geometric and arithmetic mean. The harmonic mean is calculated by dividing the number of the reciprocal by the sum of the reciprocal values....

Harmonic Mean Formula

The harmonic mean of the data set is calculated using the formula, Let x1, x2, x3, x4, … xn is the n terms of the given data then the Harmonic Mean of the given data can be calculated by the formula,...

Harmonic Mean Example

We can understand the concept of the harmonic mean by studying the example discussed below....

Relation Between AM, GM, and HM

The relation between AM, GM, and the HM of the data set is that the square of the geometric mean is equal to the product of the arithmetic mean and the harmonic mean....

How to Find Harmonic Mean?

The harmonic mean of the data set can easily be found using the steps discussed below,...

Harmonic Mean Vs Geometric Mean

Harmonic mean and Geometric mean are the measure of the central tendencies they are both Pythagorean mean and the basic difference between them is discussed in the table below,...

Harmonic Mean vs Arithmetic Mean

Harmonic mean and Arithmetic mean are the measure of the central tendencies they are both Pythagorean mean and the basic difference between them is discussed in the table below,...

Advantages and Disadvantages of Harmonic Mean

Harmonic mean is usually used in mathematics to find the average rate of change of the variables and the advantages and the disadvantages of the harmonic mean are,...

Uses of Harmonic Mean

Harmonic mean is widely used in finance, risk analysis, and insurance industries. Some of the uses of harmonic mean in real-life scenarios are,...

Solved Examples on Harmonic Mean

Example 1: Find the Harmonic Mean for the data 10, 20, 5, 15, 10....

FAQs on Harmonic Mean

Q1: What is Harmonic Mean in Statistics?...