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Dispersion

The standard deviation is a good characteristic of normal distribution on the mathematical plan, but it is not really intuitively equivalent.  We therefore prefer to use the term “dispersion” that corresponds to:

Dispersion = width of the interval value within which we observe 999.73% of values;

With a normal distribution the dispersion is calculated simply :

The concept of dispersion is much more intuitive than standard deviation. Let us take the example using the following data. An observation of 1000 pieces of data in a normal distribution with an average of 0 and standard deviation of 1:

If we want to intuitively characterize the dispersion of these values, we would be tempted to say that the value dispersion is around 6 as the observed values are limited between -3 and +3.

Our intuitive definition of the dispersion actually corresponds to the sample range (Range= Max – Min). However, using the range as a characteristic of a distribution has no statistical direction. Actually, the normal distribution varies from -infinity to +infinity making the range of this distribution infinite.

The dispersion corresponds to the intuitive definition of the dispersion all while having a statistical direction. This is an interval within which we will observe practically all the values, i.e. 99.7% of values.