Variance

See also: Statistical descriptions of model outputs, Standard deviation, Inter-percentile range, Mean deviation (MD)

Variance is calculated as follows:

i.e. it is the average of the squared distance of all generated values from their mean. The larger the variance, the greater the spread will be. The variance is called the second moment (because of its square term) about the mean and has units that are the square of the variable. So, if the output is in Ј, the variance is measured in Ј2, making it difficult to have any intuitive feel for the statistic.

Since the distance between the mean and each generated value is squared, the variance is far more sensitive to the data points that make up the tails of the distribution. For example, a data point that was three units from the mean would contribute nine times as much (32 = 9) to the variance as a data point that was only one unit from the mean (12 = 1).

The variance is useful if one wishes to determine the spread of the sum of several uncorrelated variables X, Y as it follows these rules:

     V(X+Y) = V(X)+V(Y)

     V(X-Y) = V(X)+V(Y)

     V(nX) = n2V(X)    
(where  n is some constant)

These formulae also provide us with a guideline of how to uniformly disaggregate an additive model so that each component provides a roughly equal contribution to the total output uncertainty. If the model sums a number of variables, the contribution of each variable to the outputs uncertainty will be approximately equal if each variable has about the same variance.

Read on:  Standard deviation

 

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