Russel-Research-Method-in-Anthropology

Univariate Analysis 577
interquartile range for this variable is between 96 and 100 men per 100
women. The mean is 100.2 and the median is 98.0—slightly skewed to the
left but quite close to a normal distribution.
Figure 19.5b shows MFRATIO with the extreme outlier excluded. Now the
mean and the median for this variable are almost identical (98.0 and 98.8) and
the distribution looks more-or-less normal. This is not a case for throwing out
outliers. It is a case for examining every variable in your data set to get a feel
for the distributions as the first step in analysis.
Figure 19.5c shows that 50% of the countries in the world had a very low
per capita gross national product. There is almost no whisker to the left of the
box, indicating that only a very few countries were below the interquartile
range. There is a long whisker to the right of the box, as well as two outliers
(asterisks) and six extreme outliers (circles). The circle farthest to the right is
Switzerland, with over $35,000 in per capita GNP. To put this in perspective,
Luxembourg had the world’s highest PCGDP in 2000, at $43,475. The United
States was seventh, at $31,746. Mozambique was at the bottom, at $92.
Mozambique came up to $1,200 in 2004, but by then, the United States had
gone up to nearly $38,000 (http://www.odci.gov/cia/publications/factbook/).
The shape of the box-and-whisker plot in figure 19.5c reflects the fact that the
world’s population is divided between the haves and the have-nots.
Finally, figure 19.5d shows that total fertility in 2000 ranged between about
2 and about 5, and that there were no outliers (that is, no cases beyond the
whiskers). This is another variable that looks like it might be normally distributed,
but notice that the median (the midline in the box) is off center to the
left. The mean for TFR is 3.14, lower than the median, which is 3.47. We need
more information. Read on.
Histograms and Frequency Polygons
Two other graphic methods are useful in univariate analysis: histograms
and frequency polygons (also called frequency curves). Frequency polygons
are line drawings made by connecting the tops of the bars of a histogram and
displaying the result without the bars. What you get is pure shape—less information
than you get with box plots or stem-and-leaf plots, but easily interpreted.
Figure 19.6 shows the histograms and frequency polygons for MFRATIO,
PCGDP, and TFR.
The histogram and frequency polygon for MFRATIO nail down what we
know from the box-plot of that variable: Most countries are in a narrow range
for this variable, but a few are real outliers. The histogram/polygon for
PCGDP removes all doubt about the shape of this variable: It is very highly
skewed to the right, with most countries at the bottom and the long tail of