Application of these 3 Means (AM, GM and HM) individuality? where can we use this? welcome with research papers?
Hello Shahul Hameed ,
There is a nice discussion of these three means and their applications in the following book.
[1] M. J. Moroney; Chapter 5 - On the Average and Scatter; in James R. Neuman (editor); The World of Mathematics, Vol. 3; Simon and Schuster; 1956; pp.1487-1511.
Regards,
Tom Cuff
Arithmetic mean is simply the average, but is sensitive to outliers. This can be smoothed out by the use of the geometric mean, which makes skewed distributions symmetrical. The harmonic mean uses reciprocal values and accounts for differences in sample sizes :)
Article Measures of central tendency: The mean
Arithmetic mean is calculated by adding all the sample values followed by dividing it by the number of samples taken... Geometric mean is the square root of the product of the values of each sample and harmonic mean is the reciprocal of the arithmetic mean of the reciprocal of the values of the sample... example calculation of AM, GM and HM of the values A, B and C will be
AM= (A+B+C)/3
GM= √A×B×C
HM= 3/ {(1/A)+(1/B)+(1/C)}
Arithmetic mean is used for calculation of average of anything because it consider all the observations like plant height, average speed when time is fixed, calculation of so many yield attributes. It is frequently used in agriculture and will be most authentic average... Geometric mean is used to calculate bacterial growth, cell division etc...if one value is zero, then whole GM value will be zero, because product of the value is used here..In case of harmonic mean, average of small value can be used like Average of rate or ratio because we have take reciprocal values of each samples whereby taking reciprocal of very small values obtained value is comparatively larger..
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