Table of Contents
What is Harmonic Mean?
Harmonic Mean – Definition:
Harmonic mean is a statistical measure that is used to find the average of a set of numbers that are related to each other. This measure is used to find the average of the reciprocals of the numbers in the set.
What is the Definition of the Term Harmonic Mean?
The harmonic mean is a mathematical calculation that is used to determine the average of a set of numbers. This calculation takes into account the reciprocals of the numbers in the set, and then finds the harmonic mean of those reciprocals. This calculation is often used when comparing two different sets of data, as it can provide a more accurate representation of the average than the arithmetic mean.
Formula of Harmonic Mean
The harmonic mean (HM) is a type of average that is used when working with data that are arranged in a series of ascending or descending values. The harmonic mean is calculated by taking the reciprocal of the average of the reciprocals of the individual values.
Concept of Harmonic Mean
The harmonic mean (HM) is a statistical measure that is used to find the central tendency of a set of data. The harmonic mean is used when the data set is symmetric and when the data is not evenly distributed. The harmonic mean is calculated by taking the reciprocals of the data set and then averaging the reciprocals.
Weighted Harmonic Mean
The weighted harmonic mean of a set of numbers is the harmonic mean of the numbers multiplied by their weights.
The weighted harmonic mean of the numbers 1, 2, and 3 is
(1 × 1) + (2 × 2) + (3 × 3) / (1 + 2 + 3)
= 1.5
Properties of Harmonic Mean
The harmonic mean is a measure of central tendency, and it is used to find the average of a set of numbers that are in harmonic sequence.
- The harmonic mean is always less than or equal to the arithmetic mean.
- The harmonic mean is always greater than or equal to the geometric mean.
- The harmonic mean is less sensitive to outliers than the arithmetic mean.
Uses of Harmonic Mean
Harmonic Mean is used to measure the central tendency of a data set.
It is also used to find the average of a data set which has been grouped.
Merits and Demerits of Harmonic Mean Merits
- The harmonic mean is less affected by outliers than the other two measures of central tendency.
- The harmonic mean can be used to compare averages that are not measured in the same unit.
- The harmonic mean is less likely to be affected by a small number of extreme values than the other two measures of central tendency.
Steps to Calculate Harmonic Mean
The harmonic mean (HM) is a type of average that is used to measure the central tendency of a data set. It is calculated by taking the reciprocal of the arithmetic mean of the data set’s reciprocals.
To calculate the harmonic mean:
1. Calculate the arithmetic mean of the data set.
2. Take the reciprocal of the arithmetic mean.
3. Calculate the harmonic mean of the data set.
