Register & enjoy the perks of a Universal College Application, Easy Process, Time-saving, and Free Contact details and Brochures.
Monthly Users
Monthly Applications
Admissions
No Result Found
Updated on 02nd March, 2023 , 4 min read
Harmonic Mean is a type of statistical average and is calculated by dividing the total number of observations by the series' reciprocal. As a result, the reciprocal of the arithmetic mean of reciprocals is the harmonic mean. A central tendency measure is a single number that describes how data clusters around a central value. To put it simply, the three measures of central tendencies are mean, median, and mode, and Harmonic Mean is a specific important category of mean.
The harmonic mean is a type of Pythagorean mean. To calculate it, divide the number of terms in a data series by the sum of all reciprocal terms. When compared to the geometric and arithmetic means, it will always be the lowest.
If we have a collection of observations denoted by x1, x2, x3,...xn. This data set's reciprocal terms will be 1/x1, 1/x2, 1/x3....1/xn. As a result, the harmonic mean formula is
HM = n / [1/x1 + 1/x2 + 1/x3 + ... + 1/xn]
In this case, the total number of observations is divided by the sum of all observations' reciprocals.
People also read - Mean, Median & Mode.
If the given data values are a, b, c, d,..., then the steps to find the harmonic mean are as follows:
Step 1: Determine the reciprocal of each value (1/a, 1/b, 1/c, 1/d, and so on).
Step 2: Calculate the average of the reciprocals obtained in step 1.
Step 3: Finally, find the reciprocal of the average from step 2.
|
Harmonic Mean |
Arithmetic Mean |
|
The sum of a group of numbers divided by the total number of the group of numbers is the arithmetic mean. |
The reciprocal of the average of the reciprocals of the data values is the harmonic mean. |
|
H.M is calculated by dividing the number of observations, or series entries, by the series' reciprocal. |
The arithmetic mean, on the other hand, is simply the sum of a series of numbers divided by the number of numbers in that series |
|
Harmonic Mean = n / [(1/a1)+(1/a2)+(1/a3)+…+(1/an)] |
Arithmetic Mean = (a1 + a2 + a3 +…..+an ) / n |
Pythagorean means are three means: arithmetic mean, geometric mean, and harmonic mean. The following are the formulas for three different types of means:
Arithmetic Mean = (a1 + a2 + a3 +…..+an ) / n
Harmonic Mean = n / [(1/a1)+(1/a2)+(1/a3)+…+(1/an)]
Geometric Mean = a1.a2.a3…ann
If G is the geometric mean, H is the harmonic mean, and A is the arithmetic mean, their relationship is as follows:
G=AH
Or
G2 = A.H
Let's say that we want to determine the harmonic mean of a and b. Both a and b are positive integers. Hence, by applying the aforementioned formula, we obtain,
n = 2
HM = 2 / [1/a + 1/b]
HM = (2ab) / (a + b)
The harmonic mean has the following characteristics:
The harmonic mean has the following advantages:
The harmonic series has the following drawbacks:
A useful property of harmonic mean is that it can be used to find multiplicative and divisor relationships between fractions without requiring a common denominator. This can be a very useful tool in industries such as finance. Some other real-world applications of harmonic mean are listed below.
Was this Article Helpful/Relevant or did you get what you were looking for ?
👍 1,234
👎234
The reciprocal of the average of the reciprocals of the given data values is referred to as the harmonic mean.
The following are the steps to calculate the harmonic mean: 1: Determine the values’ reciprocals. 2: Determine the average for the reciprocals obtained in step 1. 3: Next, determine the reciprocal of the average from step 2 to arrive at the final result.
The harmonic mean is most effective when applied to fractions like rates or multiples. Financial data like price multiples like the price-to-earnings (P/E) ratio are averaged using harmonic means. Market analysts may also employ harmonic techniques to spot patterns like Fibonacci sequences.
By dividing the total number of observations, or series entries, by the inverse of each series number, the harmonic mean is determined. The arithmetic mean, on the other hand, is determined by summing a set of numbers and dividing the result by the total number of numbers in the set. The reciprocal of the arithmetic mean of the reciprocals is the harmonic mean.
The harmonic mean is obtained by taking the reciprocal of the arithmetic mean of the reciprocal terms in a data set. Additionally, if each observation has a set of weights, we can calculate the weighted harmonic mean.
One measure of central tendency is the harmonic mean, which is represented as n / [1/x1 + 1/x2 + 1/x3 +... + 1/xn]. Similarly the weighted harmonic mean formula is ∑ni=1wi∑ni=1wixi∑i=1nwi∑i=1nwixi.
communication@collegesearch.in
+91 84482 99862 
Download Brochure
