In the equation above, i is the index that refers to the location of a value in a set, x i is an individual value, and N is the total number of values. The equation for calculating the geometric mean is as follows: Unlike the arithmetic mean, any given percentage change in the geometric mean has the same effect on the geometric mean. The geometric mean accounts for this by normalizing the ranges being averaged, resulting in none of the ranges dominating the weighting.
If the arithmetic means were used, the safety of the vehicle would be given far more weight, since a small percentage change on a larger scale will result in a larger difference than a large percentage change on a smaller scale a change of fuel efficiency rating from 2 to 5 which is a 250% increase in rating would be overshadowed by a 6.25% rating change of 80 to 85 if only the arithmetic mean were considered. Imagine a car that is rated on a scale of 0-5 for fuel efficiency, and a scale of 0-100 for safety. The geometric mean is useful in cases where the values being compared vary largely. This is in contrast to the arithmetic mean that performs the same function using the sum of the values in the set rather than their products. The geometric mean in mathematics is a type of average that uses the product of the values in a set to indicate central tendency. σ) and square the value to obtain the variance. Simply ensure that the correct standard deviation is being used ( s vs. Note that while the computation of variance is not explicitly shown, it is calculated as the standard deviation squared, or σ 2.
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Visit the hyperlinks provided for more detail on how to calculate these values, as well as basic examples and applications of each. Many of these values are more well described in other calculators also available on this website. Above is a simple, generalized statistics calculator that computes statistical values such as the mean, population standard deviation, sample standard deviation, and geometric mean among others.
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