# Descriptive Statistics - Variability - Example

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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