Indicators of variations
Calculation of variation  the coefficient of variation, dispersion, mean square deviation, etc.
User Maria asked me to make this calculator: /680/
The calculations in this calculator are not so hard, so here it is. Traditionally, the theory is below the calculator.
Population of analysis
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Variation  it is a difference of individual values any indication within the target population.
For example, we have a class of students  target population, and they have an annual rating of the Russian language. Somebody have an A, somebody have a B and so on. Set of these ratings throughout the class, along with their frequency ( i.e. the occurrence, for example, 10 persons have an "A", 7 persons have a  "B", 5 persons  "C") that is a variation on which you can calculate a lot of indicators.
That's what we will do.
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Absolute indicators

Range of variability  the difference between the maximum and minimum of attribute value
 Mean deviation  the arithmetic mean deviation of individual values from the mean
,
where  occurrence frequency of .
If there are too many individual values, the data can be simplified for calculations by grouping i.e. combined into intervals.
Then have meaning of iinterval or have a mean observation on iinterval.
 Dispersion  the average of the squared deviationsзначений of characteristic values of the average.
Dispersion can also be calculated the following way:
, where
 Mean square deviation  , root of dispersion
Relative indicators
Absolute indicators are measured in the same magnitude as the indicator itself and show the absolute size of deviations, therefore they are inconvenient to use for comparison the variability of different population indicators. Therefore, relative indicators of variations are calculated additionally.

Oscillation coefficient  it characterizes the variability of extreme values of indicators around the arithmetic mean.

Relative linear deviation или linear coefficient of variation  it describes the proportion of the average value out of arithmetical mean
 Variation coefficient  It characterizes the degree of homogeneity of the population, the most frequently used indicator.
The population is considered to be homogenous at values less than 40%. For values greater than 40% indicate the large indicator oscillation and it's considered to be inhomogeneous.
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