it is one of the 3 most critical imperative tendency kinds, along with the mathematics & geometric imply. The harmonic suggest represents the valuable tendency with the aid of dividing the overall integers with the sum of the integers. it's far the reciprocal of the mathematics mean. It indicates the bottom cost amongst all the means. it's miles sometimes called subcontrary mean.
$$ H = \frac {n}{\frac {1}{x_1} + \frac {1}{x_1} + . . . + \frac {1}{x_1}} = \frac {n}{\sum_{i=1}^n \frac {1} {x_i}}$$ Where, \(n\) is the total number of values and \(x (x_1, x_2 ,x_3,………,x_n)\) are the numbers in the data set.
If the set of weights \(\omega_1, \omega_2, \omega_3, . . . \omega_n\) is associated with data sets of \(x_1, x_2, x_3… x_n\), then the weighted harmonic mean of data set will be equal to:
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The harmonic suggest constantly gives the shortest price from all the different method. Its relation with the opposite means (arithmetic & Geometric) is as observe:
\(A.M > G.M > H.M\)
when you have handiest integers, you could also compute the harmonic suggest from the ratio of squared geometric suggest and mathematics imply.
\(H.M = \frac {G.M^2}{A.M}\)
Get this free on-line geometric mean calculator to determine the geometric suggest for any date set of numbers or percentages.
The method used for the calculation is as comply with:
$$ H = \frac {n}{\frac {1}{x_1} + \frac {1}{x_1} + . . . + \frac {1}{x_1}} = \frac {n}{\sum_{i=1}^n \frac {1} {x_i}}$$
allow’s have an example to better recognize the idea:
For example:
Find the harmonic mean between \(12, 23, 34, 45,\) and \(56\)?
Solution:
Here,
\(n = 5\) \(x_1= 12\) \(x_2 = 23\) \(x_3= 34\) \(x_4 = 45\) \(x_5 = 56\)
So,
\(H.M = \frac {5}{\frac {1}{12}+\frac{1}{23}+\frac {1}{34}+\frac {1}{45}+\frac {1}{56}}\)
\(H.M = \frac {5}{(0.083)+(0.043)+(0.029)+(0.022)+(0.017)}\)
\(H.M = \frac {5}{0.194}\)
\(H.M = 25.47\)
For the calculation among n numbers, divide the reciprocals of the numbers with general numbers for which you need to calculate the harmonic suggest. it is the reciprocal of mathematics imply.
To calculate the harmonic mean between n numbers in excel, use the HARMEAN function in excel. The syntax of the function is:
\(=HARMEAN\) \((number1, [number2]…)\)
There are two harmonics within the waves. they are:
1. Even harmonics.
2. Strange harmonics.
