Mean (x)

See also: Median, Mode, Statistical descriptions of model outputs, Presenting results introduction

This is the average of all the generated output values. It has less immediate intuitive appeal than the mode or median but it does have far more value. One can think of the mean of the output distribution as the x-axis point of balance of the histogram plot of the distribution. The mean is also known as the expected value though we don't recommend using the term as it implies for most people the mode (i.e. the value with the highest probability). The mean is sometimes also known as the first moment about the origin, which engineers will recognise from the idea of a turning moment about the origin. The mean of a data set {xi} is often given the notation x. It is particularly useful for the following two reasons:

         (a+b) = a + b          and therefore  (a-b) = a - b
 

         (a*b) = a * b  

where a and b are two independent stochastic variables. In other words: 1) the mean of the sum is the sum of their means; and 2) the mean of their product is the product of their means. These two results are very useful if one wishes to combine risk analysis results (e.g. from partial models) or look at the difference between them.

Read on: Relative positioning of mode median and mean

 

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