Russel-Research-Method-in-Anthropology

172 Chapter 7
mode 1 mode 2 mode mean mean mode
mean
median
median
median
a. Bimodal distribution b. Skewed to the right c. Skewed to the left
Figure 7.2. Bimodal and skewed distributions.
Figure 7.2b and figure 7.2c are skewed distributions. A distribution can be
skewed positively (with a long tail going off to the right) or negatively (with
the tail going off to the left). Figures 7.2b and 7.2c look like the distributions
of scores in two very different university courses. In figure 7.2b, most students
got low grades, and there is a long tail of students who got high grades. In
figure 7.2c, most students got relatively high grades, and there is a long tail of
students who got lower grades.
The normal distribution is symmetric, but not all symmetric distributions
are normal. Figure 7.3 shows three variations of a symmetric distribution—
a. A leptokurtic distribution b. A normal distribution c. A platykurtic distribution
Figure 7.3. Three symmetric distributions including the normal distribution.
that is, distributions for which the mean and the median are the same. The one
on the left is leptokurtic (from Greek, meaning ‘‘thin bulge’’) and the one on
the right is platykurtic (meaning ‘‘flat bulge’’). The curve in the middle is the
famous bell-shaped, normal distribution. In a leptokurtic, symmetric distribution,
the standard deviation is less than 1.0; and in a platykurtic, symmetric
distribution, the standard deviation is greater than 1.0. The physical distance
between marriage partners (whether among tribal people or urbanites) usually
forms a leptokurtic distribution. People tend to marry people who live near
them, and there are fewer and fewer marriages as the distance between partners
increases (Sheets 1982). By contrast, we expect the distribution of height
and weight of athletes in the National Basketball Association to be more platykurtic
across teams, since coaches are all recruiting players of more-or-less
similar build.
The shape of a distribution—normal, skewed, bimodal, and so on—contains