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Descriptive Statistics - Variability - Example

[Home] [Up] [Central Tendency] [Concentration] [Box Plot] [Density Trace] [Frequency Table] [Moments] [Correlation] [Partial Correlation] [Quartiles] [Simple Regression] [Histogram] [Skew./Peaked.] [Rank Correlation] [Variability]

[Range] [Variance] [Standard Deviation] [Variation] [MSE] [MSE vs Variance] [Variation vs Herfindahl] [Mean AD] [Median AD] [Quartiles] [Observations] [Comparison] [Gini Mean Difference] [Leik's D] [Dispersion] [Diversity] [Qualitative Variation] [Mean Sq Deviation] [Relationships]

Data

Airline Data ()

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Output

+-----------------------------------------+
 VAMUND : VARIABILITY 1 - UNGROUPED DATA 
+-----------------------------------------+

                             Biased      Unbiased

Variance               :     1.4292        1.4392
Standard Deviation     :     1.1955        1.1997
Coeff. of Variation    :      .4265         .4280

Mean Absol. Deviation  :     1.0044

Quartile        First  :     1.8000
                Third  :     3.6050
Semi-Interquart.Range  :      .9025
     Interquart.Diff.  :     1.8050
Coeff. of Quart. Var.  :      .3340

Smallest  Value        :     1.0400
Largest   Value        :     6.2200
Range        Absolute  :     5.1800
           Normalized  :     4.3329        4.3179

Number of Observations :   144
+-----------------------------------------+
 VAMUND : VARIABILITY 2 - UNGROUPED DATA 
+-----------------------------------------+

Arithmetic Mean                              :     2.8030
Biased Variance                              :     1.4292
Biased Standard Deviation                    :     1.1955

Mean of Sq.  Diff. for Pairs of Observations :     2.8784
Mean of Abs. Diff. for Pairs of Observations :     1.3591

GINI's Mean Difference                       :     1.3591

Number of Observations                       :   144
Number of Pairs of Differences               : 10296
+-----------------------------------------+
 VAMUND : VARIABILITY 3 - UNGROUPED DATA 
+-----------------------------------------+

Range                                  :     5.1800
Variance                  Biased Value :     1.4292
                               Maximum :     6.7081
Standard Deviation        Biased Value :     1.1955
                               Maximum :     2.5900

Mean   Squared  Deviations from   Mean :     1.4292
Mean   Squared  Deviations from Median :     1.4511
Mean   Absolute Deviations from   Mean :     1.0044
                               Maximum :     2.5900
                               Minimum :      .0360
Mean   Absolute Deviations from Median :      .9955
             Coefficient of Dispersion :      .3749
Median Absolute Deviations from   Mean :      .9300
Median Absolute Deviations from Median :      .9000
LEIK's Measure of Dispersion           :      .4565
Index of Diversity               Value :      .9918
                               Maximum :      .9931
Index of Qualitative Variation         :      .9987
Number of Observations                 :   144

() Box, G.E. and Jenkins, G.M.

Time Series Analysis : Forecasting and Control

Holden Day, San Francisco, 1976, p. 531.

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Home
Up
Central Tendency
Concentration
Box Plot
Density Trace
Frequency Table
Moments
Correlation
Partial Correlation
Quartiles
Simple Regression
Histogram
Skew./Peaked.
Rank Correlation
Variability
Range
Variance
Standard Deviation
Variation
MSE
MSE vs Variance
Variation vs Herfindahl
Mean AD
Median AD
Quartiles
Observations
Comparison
Gini Mean Difference
Leik's D
Dispersion
Diversity
Qualitative Variation
Mean Sq Deviation
Relationships
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