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Harmonic mean of a grouped sample.



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In some scientific works, once the data have been gathered from a population of interest, it is often difficult to get a sense of what the data indicate when they are presented in an unorganized fashion.
Assembling the raw data into a meaningful form, such as a frequency distribution, makes the data easier to understand and interpret. It is in the context of frequency distributions that the importance of conveying in a succinct way numerical information contained in the data is encountered.

So, grouped data is data that has been organized into groups known as classes. The raw dataset can be organized by constructing a table showing the frequency distribution of the variable (whose values are given in the raw dataset). Such a frequency table is often referred to as grouped data.

The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of the evaluated values. It should be employed in averaging any rates (value related to any unit: averaging rate metrics). The harmonic mean is best used in situations where extreme outliers exist in the population. Because the harmonic mean is unintuitive, it is hard to see how to apply it in practical situations. Two examples where the harmonic mean is absolutely necessary are variable-speed processors and load balancing servers.

According to Jensen (1998), one can define the power mean, p-norm, or generalized mean

Mp = [E[x^p]]^(1/p)

which reduces to the harmonic, geometric and arithmetic means for p = -1, p -> 0 (eg. 1/2,1/3,1/4,..1/20000,..,1/n) and p = 1, respectively.

Here, we developed a m-code to calculate the harmonic mean of a grouped data.

One can input the returns or modified vectors n and xout containing the frequency counts and the bin locations of the hist m-function, in a column form matrix.

Harmonic mean calculation uses the formula,
H = N/Sum(Fi/MCi)

Fi = class frequency
MCi = class mark
N = sample size [sum(Fi)]

Syntax: function y = gharmmean(x)
x - data matrix (Size of matrix must be n-by-2; absolut frequency=column 1, class mark=column 2

y - harmonic mean of the values in x

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