Russel-Research-Method-in-Anthropology

576 Chapter 19
Box-and-Whisker Plots
Stem-and-leaf plots give you exact values for the median, the hinges of the
interquartile range, and the cases in the tails of a distribution. Box-andwhisker
plots (or, simply, box plots) throw out the details and show you just
the shape of a distribution. Together, the quantitative data from a stem-andleaf
plot and the purely qualitative image of a box plot give you a lot of useful
information.
Figure 19.5 shows the box plots for MFRATIO (with and without the outliers),
PCGDP and TFR. The boxes themselves show you the interquartile
**
*
50 100 150 200
a. MFRATIO (all values)
90 95 100 105 110
b. MFRATIO (excluding the extreme outlier)
**
0 10,000 20,000 30,000 40,000
c. PCGDP
1 2 3 4 5 6 7
d. TFR
Figure 19.5. Box-and-whisker plots for four social indicators of 50 countries (from
Table 19.8).
range—the middle 50% of the cases. The vertical line that marks off the box
at the left is the 25th percentile (the lower hinge) of the plot; the vertical line
that marks off the box at the right is the 75th percentile (the upper hinge). The
vertical line inside the box is the median, or the 50th percentile. Fifty percent
of the cases in the distribution fall to the right of the median line and 50% fall
to the left.
The whiskers in box plots extend one-and-a-half times the interquartile
range from the lower and upper hinges of the box. When data are normally
distributed, this will be about 2.7 standard deviations from the mean. Cases
outside that range are outliers and are marked by an asterisk. Cases that are
more than three times the interquartile range from the hinges are extreme outliers
and are marked by little circles.
The box plot for MFRATIO (figure 19.5a) shows that, in 50% of the countries
of the world, the interquartile range is a very, very narrow band, with
very, very short whiskers, a few outliers, and one extreme outlier. In fact, the