= Σ = . Table : . G M Anti N log log Σ Anti log Anti log . GM = .
Example . Compute the Geometric mean from the data given below: Marks - - - - - No. of Students Marks m log m f log m - . .
N = Σ f m log = . Table : . G M Anti m N log log Σ Anti log Anti log . GM = .
Specific uses of Geometric mean The most useful application of geometric mean is to average the rate of changes. For example, from to prices increased by %, % and % respectively. The average annual increase is not % as given by the arithmetic average but . % as obtained by the geometric mean.
This average is also useful in measuring the growth of population, because population increases in geometric progression. Example . Compared to the previous year the overhead expenses went up by % in , they - - Descriptive statistics and probability increased by % in the next year and by % in the following year. Calculate the average rate of increase in overhead expenses over the three years.
In averaging ratios and percentages, geometric mean is more appropriate. Let us consider X represents Expenses at the end of the year. % Rise log X . .
. log . Σ Table : . GM Anti log log Σ Anti log .
Anti log . GM = . Average rate of increase in overhead expenses . – = .
% Geometric mean cannot be calculated