Dispersion Measure

A Dispersion Measure is a measure of how stretched or squeezed a probability distribution is.

• AKA: Variability Measure, Scatter Measure, Spread Measure.
• Context:
  • It can produce a Dispersion Value.
  • …
• Example(s):
  • a Statistical Variance (σ²).
  • a Standard Deviation (SD).
  • a Standard Error (SE).
  • a Sum of the Squares (SS).
  • a total Statistical Range.
  • a Interquartile Range.
  • a Gini Index.
  • …
• Counter-Example(s):
  • Mean.
  • Median.
  • Mode.
• See: Central Tendency Metric, Variance Metric, Scatterplot Diagram, Statistical Sample.

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References

2016

• (Changing Minds website, 2016) ⇒ http://syque.com/quality_tools/toolbook/Variation/measuring_spread.htm
  • QUOTE: There are two main ways of measuring the degree of spread of a set of measurements: the range and the standard deviation.

Range

The range of a set of measures is simply the difference between the largest and the smallest measurement value.

Thus, for example, if you have a set of measures (21, 22, 26, 19, 12, 24, 33) then you first find the highest measure (33) and subtract the lowest measure (12) to give the range (21). This is easy to calculate, but there can be several problems with using it:

• Special causes of variation can cause an unrealistically wide range.
• As more measurements are made, it will tend to increase.
• It gives no indication of the data between its values.

Standard deviation

The standard deviation is a number which is calculated using a simple mathematical trick (calculating the square root of the average of squares) to find an 'average' number for the distance of the majority of measures from the mean.

The standard deviation is of particular value when used with the Normal distribution, where known proportions of the measurements fall within one, two and three standard deviations of the mean (...)=== 2013 ===

• http://en.wikipedia.org/wiki/Statistical_dispersion
  • In statistics, dispersion (also called variability, scatter, or spread) denotes how stretched or squeezed is a distribution (theoretical or that underlying a statistical sample). Common examples of measures of statistical dispersion are the variance, standard deviation and interquartile range.

    Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.

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