Geometric Means Calculator Geometric Means Calculator Geometric Mean of any series which contains N observations is the Nth root of the product of the values. If there are two values, then the square root of the product of the values is called the geometrical mean. In case there are three values, then the cube root of the values is the geometrical mean. Let us look at the ungrouped data and find how to find the geometrical Mean of the ungrouped data. Geometric Mean Calculator help us to calculate G. M. In such cases we say that the Geometrical Mean = nth root ( the product of n values ) To do such calculations we use the logarithms and so it can be written as follows : Log (G.M. ) = (1/n ) * ( log(x1. X2 . x3 .x4 …… xn) ), = ( 1/ n) [ log x1 + log x2 + log x3 + log x4 + log x5 …… + log xn ] Thus we conclude that the G.M. of a set of observations is the arithmetic mean of their logarithm values .
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It can also be written by taking the antilogarithm on both sides of the equation : G.M. = Antilog [ 1/ n * Σ log X ] Let us look at the Algebraic properties of Geometric Mean: 1. As it is in the case of Arithmetic Average, the sum of the items remains unchanged if each item is replaced by the Arithmetic Average the product of the items remain unchanged in case of G.M. if each item is replaced by geometric mean. 2.
It is a suitable tool used for further mathematical treatment.
Following are some of the merits of G. M.: 1.
The G. M. is rigidly defined and its value is precise.
2.
It is based on all the observations in the series.
3.
It is suitable for further mathematical treatment.
4. Unlike A. M. , Geometric mean is not effected mush by the presence of either extremely small or extremely large values in the data collected. 5. It is also not mush effected by the fluctuations in the raw sample data collected from the survey. It gives comparative more weight to the lower values. Here are some of the drawbacks of the Geometrical Mean : 1.
It is neither easy to calculate nor simple to understand by an ordinary man.
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2. Like Arithmetic mean, Geometric Mean can be any one of the value, which does not exist in the series of sample collected. 3. If any value in the series is zero, the Geometric Mean would also be zero. It can also be an imaginary value if any one of the observation is negative. 4. The property of giving more weight to the smaller items may be in some of the cases prove to be the drawback of the geometrical mean. In many cases smaller items have to be given smaller weight and bigger items are given bigger weights. In such situations we say that the geometrical mean is not the appropriate and ideal average to be calculated and to be considered.
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