Page 91 - Statistics for Dummies

Chapter 5: Means, Medians, and More
those superstar players and report the average. But if you’re on the side of
the players, you would want to report the median, because that’s more rep-
resentative of what the players in the middle are making. Fifty percent of the
players make a salary above the median, and 50 percent make a salary below
the median. To sort it all out, it’s best to find and compare both the mean
and the median. A graph showing the shape of the data is a great place
to start.

One of the graphs you can make to illustrate the shape of numerical data (how
many values are close to/far from the mean, where the center is, how many
outliers there might be) is a histogram. A histogram is a graph that organizes
and displays numerical data in picture form, showing groups of data and the
number or percentage of the data that fall into each group. It gives you a nice
snapshot of the data set. (See Chapter 7 for more information on histograms
and other types of data displays.)
Data sets can have many different possible shapes; here is a sampling of
three shapes that are commonly discussed in introductory statistics courses: 75
✓ If most of the data are on the left side of the histogram but a few larger
values are on the right, the data are said to be skewed to the right.
Histogram A in Figure 5-1 shows an example of data that are skewed to
the right. The few larger values bring the mean upwards but don’t really
affect the median. So when data are skewed right, the mean is larger than
the median. An example of such data is NBA salaries.
✓ If most of the data are on the right, with a few smaller values showing up
on the left side of the histogram, the data are skewed to the left.
Histogram B in Figure 5-1 shows an example of data that are skewed
to the left. The few smaller values bring the mean down, and again the
median is minimally affected (if at all). An example of skewed-left data is
the amount of time students use to take an exam; some students leave
early, more of them stay later, and many stay until the bitter end (some
would stay forever if they could!). When data are skewed left, the mean
is smaller than the median.
✓ If the data are symmetric, they have about the same shape on either side
of the middle. In other words, if you fold the histogram in half, it looks
about the same on both sides.
Histogram C in Figure 5-1 shows an example of symmetric data in a his-
togram. With symmetric data, the mean and median are close together.
By looking at Histogram A in Figure 5-1 (whose shape is skewed right), you
can see that the “tail” of the graph (where the bars are getting shorter) is
to the right, while the “tail” is to the left in Histogram B (whose shape is
skewed left). By looking at the direction of the tail of a skewed distribution,
you determine the direction of the skewness. Always add the direction when
describing a skewed distribution.

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