Interquartile Range, etc.
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Author:   Lawrence C. Hamilton, Dept. of Sociology, Univ. of New Hampshire
Support:  None. 

		^iqr^ varname [^if^ exp] [^in^ range]

The command provides the following output:

      number of observations       mean           10 trim
      standard deviation           median         IQR
      pseudo standard deviation    
      
      (for both) low and high:
      inner fences                 outer fences
          # mild outliers              # severe outliers
          % mild outliers              % severe outliers



      
Definitions
-----------

      IQR (Interquartile Range) = 75th percentile - 25th percentile
      Pseudo standard deviation = IQR/1.349
      10% trim mean             = Average of cases between 10th and
                                     90th percentiles
      Inner fences              = Q(25)-1.5IQR and Q(75)+1.5IQR
      Outer fences              = Q(25)-3IQR   and Q(75)+3IQR
      Mild outlier              = Q(25)-3IQR <= x < Q(25)-1.5IQR  or
                                  Q(75)+1.5IQR < x <= Q(75)+3IQR
      Severe outlier            = x < Q(25)-3IQR  or  x > Q(75)+3IQR

Notes:
------

In a symetrical distribution, the trimmed mean equals median and mean.

Values beyond the inner fences make up about 0.7% of normal population.

Severe outliers comprise about .0002% of the normal population. In 
samples, they lie far out enough to have a substantial effect on means,
standard deviations, and other classical statistics.

The presence of any severe outliers in a real-data sample of n=10 to at
least 300 should be sufficient evidence to reject normality at a 5%
significance level. Mild outliers appear common in samples of any size.