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gharmmean

gharmmean

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01 Oct 2012 (Updated )

Harmonic mean of a grouped sample.

gharmmean(x)
function y = gharmmean(x)
%GHARMMEAN Harmonic mean of a grouped sample.
%  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)
%
%  where:
%  Fi  = class frequency
%  MCi = class mark
%  N   = sample size [sum(Fi)]
%  
%  Syntax: function y = gharmmean(x) 
%      
%  Inputs:
%       x - data matrix (Size of matrix must be n-by-2; absolut frequency=
%           column 1, class mark=column 2) 
%  Outputs:
%       y  - harmonic mean of the values in x
%
%  Example: Suppose we have the next frequency table:
%
%                     ----------------
%                       MC         F
%                     ----------------
%                      34.5        2
%                      44.5        3
%                      54.5       11
%                      64.5       20
%                      74.5       32
%                      84.5       25
%                      94.5        7
%                     ----------------
%
%  Taken from: 
%  http://www.emathzone.com/tutorials/basic-statistics/harmonic-mean.html
%
%  Where we are interested to get the harmonic mean value.
%
%  Data input:
%  x = [34.5 2;44.5 3;54.5 11;64.5 20;74.5 32;84.5 25;94.5 7];
%
%  Calling on Matlab the function: 
%          y = gharmmean(x)
%
%  Answer is:
%
%  y = 69.6010
%
%  Created by A. Trujillo-Ortiz, R. Hernandez-Walls,
%             O.A. Mancillas-de-la-Torre and S. Alvarez-Borrego*
%             Facultad de Ciencias Marinas
%             Universidad Autonoma de Baja California
%             Apdo. Postal 453
%             *Centro de Investigacion Cientifica y de Educacion Superior
%             de Ensenada, Carr. Ens-Tij 3918 Zona Playitas
%             Ensenada, Baja California
%             Mexico.
%             atrujo@uabc.edu.mx
%
%  Copyright (C)  September 24, 2012.
%
%  To cite this file, this would be an appropriate format:
%  Trujillo-Ortiz, A., R. Hernandez-Walls, O.A. Mancillas-de-la-Torre and
%     S. Alvarez-Borrego. (2012). gharmmean:Harmonic mean of a grouped 
%     sample. [WWW document]. URL http://www.mathworks.com/matlabcentral/
%     fileexchange/38441-gharmmean
%
%  Reference:
%  Agarwal, B. L. (2006), Basic Statistics. 4th Ed. New Age International 
%           Ltd., Publishers. Daryaganj:New Delhi.
%  Jensen, J. L. (1998), Some statistical properties of power averages for
%           lognormal samples. Water Resour. Res. 34(9):2415-2418.
%

c = size(x,2);

if c ~= 2
    error('stats:gharmmean:BadData','X must have two colums.');
end

mc = x(:,1); %class mark
f = x(:,2); %absolut frequency
n = sum(f); %sample size
y = n/sum(f./mc);

return,

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