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.
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.
