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Symmetry and Skewness

The shape of the data is often described by its symmetry or nonsymmetry (also called skewness ). Here are stem-and-leaf plots for symmetric , right skewed, and left-skewed data.



  SYMMETRIC DATA           RIGHT-SKEWED DATA        LEFT-SKEWED DATA


     4 | 7                    4 | 58                   4 | 0 
     5 | 35                   5 | 011245569            5 | 5
     6 | 005                  6 | 2445                 6 | 2
     7 | 11200                7 | 17                   7 |
     8 | 846799               8 |                      8 | 17
     9 | 0199                 9 | 2                    9 | 2445
    10 | 41                  10 | 5                   10 | 011245569
    11 | 1                   11 | 0                   11 | 58



The term `skew' refers to the direction of the longer tail if you stand the stem-and-leaf upright, or draw a histogram. Here is the histogram of the left-skewed stem plot above.





Histogram of left-skewed data




\epsfig{file=hist.eps}




The long tail, of course, denotes outlying  or extreme  observations. The left-skewed histogram above contains outlying small observations, while a right-skewed histogram would have outlying large observations. A left skew also indicates that the smallest quarter of observations will be more spread out. See the boxplot below.





Boxplot of left-skewed data




\epsfig{file=box2.eps}







2003-09-08