


Geometric mean
Geometric mean in math is a type of mean or average, which denotes the central tendency or typical value of a set of numbers. In other words, it is a measure of central tendency, just like median. It is different from Arithmetic mean, because the numbers are multiplied, and the nth root of resulting product is taken. If x_{1}, x_{2}, x_{3},.....x_{n} are the numbers for which we have to find the G.M G, then In other words G.M is the nth root of the product of n values in the data. G.M is used often in comparing different items, when each item has multiple properties that have different numeric ranges. G.M is often useful for highly skewed data. It is also natural for summarizing ratios. Note: We should not use G.M if, the data has any negative values. Examples: 1. Find the G.M of 5,7,3,1. Solution: By definition, the G.M is the 4th root of product of 5,7,3 and 1. G = ^{4}√5x7x3x1 =^{4}√105 =3.2011 2. Find the geometric mean of 1/2 and 40. Solution: By definition, G.M of 1/2 and 40 is the square root of product of 1/2 and 40. G = √(1/2)x40 =√20 =2√5 =4.4721 1. Find 5 geometric means between 576 and 9 Solution:
Let G_{1},G_{2},G_{3},G_{4},G_{5} Here the last term is G_{6}= 576 r^{6} G_{1} = ar = 576(1/2) = 288 G_{2}= ar^{2} = 576 (1/2)^{2} = 576 x (1/4)= 144 G_{4}= ar^{4} = 576 (1/2)^{4} = 576 (1/16) = 36
G_{5}= ar^{5} = 576 (1/2)^{5} = 576 (1/32) = 18

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