Page 123 - Statistics for Dummies

Chapter 7: Going by the Numbers: Graphing Numerical Data
✓ The amount of variability in the data (statisticians call this the amount
of spread in the data)
✓ Where the center of the data is (statisticians use different measures)
Checking out the shape of the data
One of the features that a histogram can show you is the shape of the data —
in other words, the manner in which the data fall into the groups. For exam-
ple, all the data may be exactly the same, in which case the histogram is just
one tall bar; or the data might have an equal number in each group; in which
case the shape is flat.
Some data sets have a distinct shape. Here are three shapes that stand out:
✓ Symmetric: A histogram is symmetric if you cut it down the middle and
the left-hand and right-hand sides resemble mirror images of each other.
Figure 7-2a shows a symmetric data set; it represents the amount of time

each of 50 survey participants took to fill out a certain survey. You see 107
that the histogram is close to symmetric.
✓ Skewed right: A skewed right histogram looks like a lopsided mound,
with a tail going off to the right.
Figure 7-1, showing the ages of the Best Actress Award winners, is
skewed right. You see on the right side there are a few actresses whose
ages are older than the rest.
✓ Skewed left: If a histogram is skewed left, it looks like a lopsided mound
with a tail going off to the left.
Figure 7-2b shows a histogram of 17 exam scores. The shape is skewed
left; you see a few students who scored lower than everyone else.
Following are some particulars about classifying the shape of a data set:
✓ Don’t expect symmetric data to have an exact and perfect shape. Data
hardly ever fall into perfect patterns, so you have to decide whether the
data shape is close enough to be called symmetric.
If the shape is close enough to symmetric that another person would notice
it, and the differences aren’t enough to write home about, I’d classify it as
symmetric or roughly symmetric. Otherwise, you classify the data as non-
symmetric. (More sophisticated statistical procedures exist that actually
test data for symmetry, but they’re beyond the scope of this book.)
✓ Don’t assume that data are skewed if the shape is non-symmetric.
Data sets come in all shapes and sizes, and many of them don’t have a
distinct shape at all. I include skewness on the list here because it’s one
of the more common non-symmetric shapes, and it’s one of the shapes
included in a standard introductory statistics course.
If a data set does turn out to be skewed (or close to it), make sure to
denote the direction of the skewness (left or right).

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