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st: Interpreting summarize, detail


From   Syed Basher <syed.basher@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Interpreting summarize, detail
Date   Sat, 5 Feb 2011 22:09:05 -0800 (PST)

Hello all,

I am having some difficulty in interpreting the basic summary statistics. 
Consider the following:

. sysuse auto
(1978 Automobile Data)

. summarize mpg, detail

                        Mileage (mpg)
-------------------------------------------------------------
      Percentiles      Smallest
 1%            12             12
 5%            14             12
10%           14             14       Obs                       74
25%           18             14       Sum of Wgt.          74

50%           20                           Mean            21.2973
                              Largest       Std. Dev.       5.785503
75%           25             34
90%           29             35       Variance       33.47205
95%           34             35       Skewness    .9487176
99%           41             41       Kurtosis       3.975005

In the above output, the largest value in 75% is 34, while the starting value of 
90% is 29. The same is with the 95%. Why this is so? Shouldn't the percentile 
value be monotonically increasing? I am interested in this because in one of my 
own data, I have obtained the following output:

                           uprice
-------------------------------------------------------------
      Percentiles              Smallest
 1%     .0022779         .0001697
 5%       .01875          .0002087
10%     .0581161       .0010804       Obs                 626
25%     .3826962       .0012382       Sum of Wgt.     626

50%     1.667209                                 Mean           79.44026
                                   Largest             Std. Dev.      432.1083
75%     9.730152       2658.562
90%     77.09222       3077.629       Variance       186717.6
95%     363.5599       5423.877       Skewness       11.04796
99%      1490.65       7004.734       Kurtosis       151.0011

where as you can see I have a similar problem (largest value in 75% is much 
higher than the starting value in 90% and so on). I am guessing that this is due 
to the 3rd (skewness) and 4th (kurtosis) moments of the distribution. But I do 
not have a convincing interpretation/explanation. Your help will be much 
appreciated.

Regards,

Syed Basher
Qatar National Food Security Programme



      
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