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Indicators of variations

Calculation of variation - the coefficient of variation, dispersion, mean square deviation, etc.

Traditionally, the theory is below the calculator.

PLANETCALC, Indicators of variations

Indicators of variations

Population of analysis

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Items per page:

Digits after the decimal point: 2
Arithmetic average
 
Range of variability
 
Mean deviation
 
Dispersion
 
Mean square deviation
 
Oscillations coefficient (percentage)
 
Relative linear deviation (percentage)
 
Variation coefficient (percentages)
 

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 has an A; somebody has 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.

Absolute indicators

  1. Range of variability - the difference between the maximum and minimum of attribute value
    R=x_{max}-x_{min}

  2. Mean deviation - the arithmetic mean deviation of individual values from the mean
    \bar{l}=\frac{\sum{|x_i-\bar{x}|f_i}}{\sum{f_i}},
    where f_i - occurrence frequency of x_i.

If there are too many individual values, the data can be simplified for calculations by grouping, i.e., combined into intervals.
Then x_i have meaning of i-interval or have a mean observation on i-interval.

  1. Dispersion - the average of the squared deviationsзначений of characteristic values of the average.
    \sigma^2=\frac{\sum{(x_i-\bar{x})^{2}f_i}}{\sum{f_i}}

Dispersion can also be calculated the following way:
\sigma^2=\bar{x^2}-\bar{x}^2, where \bar{x^2}=\frac{\sum{x^{2}f}}{\sum{f}}

  1. Mean square deviation - \sigma, root of dispersion

Relative indicators

Absolute indicators are measured in the same magnitude as the indicator itself and show the deviations' absolute size. Therefore they are inconvenient to use for comparing the variability of different population indicators. Therefore, relative indicators of variations are calculated additionally.

  1. Oscillation coefficient - it characterizes the variability of extreme values of indicators around the arithmetic mean.
    K_o=\frac{R}{\bar{x}}

  2. Relative linear deviation или linear coefficient of variation - it describes the proportion of the average value out of arithmetical mean
    K_l=\frac{\bar{l}}{\bar{x}}

  3. Variation coefficient - It characterizes the population's degree of homogeneity, the most frequently used indicator.
    V_\sigma=100\frac{\sigma}{\bar{x}}

The population is considered to be homogenous at values less than 40%. For values greater than 40% indicate the large indicator oscillation, it's considered inhomogeneous.

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