About Harmonic Mean Formula
The harmonic mean is a sort of numerical average that is commonly employed when calculating the average rate or rate of change. One of the three Pythagorean meanings is this. The arithmetic mean and the geometric mean are the last two. These three averages or means are crucial since they are widely used in the fields of geometry and music. The harmonic mean can be defined as reciprocal of average of reciprocal terms given a data series or a group of observations. It's the reciprocal of the arithmetic mean of the reciprocals, in other words.
What Does Harmonic Really Mean?
A measure of central tendency is the harmonic mean. Let's say we want to find a single number that may be used to explain how data behaves around a central value. The value is then referred to as a measure of central tendency. There are three types of central tendency measurements in statistics. The mean, median, and mode are the three values. The mean can be divided into three types: arithmetic, geometric, and harmonic.
Definition of Harmonic Mean
The Pythagorean mean is a sort of harmonic mean. We calculate it by multiplying 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.
Solved Example of Harmonic Mean
Assume we have a series of 1, 3, 5, and 7. Each word has a difference of two. This creates a mathematical progression. We take the reciprocal of these terms to determine the harmonic mean. This is expressed as 1, 1/3, 1/5, and 1/7. (the sequence forms a harmonic progression). The total number of phrases (4) is then divided by the sum of the terms (1 + 1/3 + 1/5 + 1/7). As a result, the harmonic mean is calculated as 4 / (1 + 1/3 + 1/5 + 1/7) = 2.3864.
Formula of Harmonic Mean
If we have a set of observations denoted by x1, x2, x3,...xn, we may use the following formula. 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]
Harmonic Mean of Two Numbers
Let's say we wish to calculate the harmonic mean of any two values in a data set, a and b. Both a and b are positive integers. As a result of applying the aforementioned formula, we obtain:
- n = 2
- HM = 2 / [1/a + 1/b]
- HM = (2ab) / (a + b)
How can we find what Harmonic Mean?
To find the harmonic mean of the terms in a given observation set, follow the techniques outlined below.
- Multiply each term in the data collection by its reciprocal.
- Count how many terms there are in the provided data set. This will be number n.
- Put all of the reciprocal terms together.
- Multiply the result of step 2 by the result of step 3. The harmonic mean of the required number of terms will be the resultant.
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