Page 127 - Statistics for Dummies

Chapter 7: Going by the Numbers: Graphing Numerical Data
Figure 7-3:
Descriptive Statistics: Age
Descriptive
statistics
for Best
Total
Q1
Maximum IQR
Actress
Mean
Median
StDev Minimum
Q3
Variable Count
28.00
83
Age
11.00
39.00
35.69
33.00
21.00
11.35
81.00
ages
(1928–2009).

Here are some tips for connecting the shape of the histogram (discussed in
the previous section) with the mean and median:
✓ If the histogram is skewed right, the mean is greater than the median.

This is the case because skewed-right data have a few large values that
drive the mean upward but do not affect where the exact middle of the
data is (that is, the median). Looking at the histogram of ages of the Best 111
Actress Award winners in Figure 7-1, you see they’re skewed right.
✓ If the histogram is close to symmetric, then the mean and median are
close to each other.
Close to symmetric means it’s almost the same on either side; it doesn’t
need to be exact. Close is defined in the context of the data; for example,
the numbers 50 and 55 are said to be close if all the values lie between 0
and 1,000, but they are considered to be farther apart if all the values lie
between 49 and 56.
The histogram shown in Figure 7-2a is close to symmetric. Its mean and
median are both equal to 3.5.
✓ If the histogram is skewed left, the mean is less than the median.
This is the case because skewed-left data have a few small values that
drive the mean downward but do not affect where the exact middle of
the data is (that is, the median).
Figure 7-2b represents the exam scores of 17 students, and the data are
skewed left. I calculated the mean and median of the original data set to
be 70.41 and 74.00, respectively. The mean is lower than the median due
to a few students who scored quite a bit lower than the others. These
findings match the general shape of the histogram shown in Figure 7-2b.
The tips for interpreting histograms found in the previous section can also be
used the other way around. If for some reason you don’t have a histogram of
the data, and you only have the mean and median to go by, you compare them
to each other to get a rough idea as to the shape of the data set.
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