Normalized measures of spread

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

Normalized measures of spread are calculated by dividing a measure of spread (except the variance because it has squared units) by a measure of location. A useful example of this is the normalized standard deviation.

The normalized standard deviation (or Coefficient of Variance) is just the standard deviation divided by the mean i.e.:

It achieves two purposes:

  1. The standard deviation is given as a fraction of its mean. Using this statistic allows the spread of the distribution of a variable with a large mean and correspondingly large standard deviation to be compared more appropriately with the spread of the distribution of another variable with smaller mean and correspondingly smaller standard deviation.

  2. The standard deviation is now independent of its units. So, for example, the relative variability of the Euro: Hong Kong Dollar and US$: Sterling exchange rates can be compared.

The normalized inter-percentile range works in the same way:

= (xB - xA) /x50

where xB > xA are percentiles like x95 and x05 respectively.

Read on: Skewness (S)

 

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