Russel-Research-Method-in-Anthropology

582 Chapter 19
Notice that we need to square the difference of each observation from the
mean and then take the square root later. As we saw in calculating the mean,
xx0. That is, the simple sum of all the deviations from the mean is
zero. Squaring each difference (each x x) gets rid of the negative numbers.
Variance describes in a single statistic how homogeneous or heterogeneous
a set of data is, and, by extension, how similar or different the units of analysis
described by those data are. Consider the set of scores in table 19.2 on the
variable called REDUCE. These scores show people’s support for the idea
that ‘‘Americans are going to have to drastically reduce their consumption
over the next few years.’’ Suppose that for each level of education, you could
predict the level of support for that attitudinal item about cutting back on consumption.
If you could do this in 100% of all cases, then you would speak of
‘‘explaining all the variance’’ in the dependent variable.
I’ve never encountered this strength of association between two variables in
the social sciences, but some things come pretty close, and in any event, the
principle is what’s important.
The standard deviation, s, is the square root of the variance, s 2 . The formula
for the standard deviation is:
s 2
xx
n1
Formula 19.5
Table 19.10 shows how to calculate the standard deviation for the data on
female illiteracy in table 19.7. The sum of the (x x) 2 is 3,896.11 and n
10.
Substituting in the formula for standard deviation, we get:
s
3,896.11
9
20.81
If we were reporting these data, we would say that ‘‘the average percentage of
adult female illiteracy is 19.49 with sd 20.81.’’
For grouped data, we take the midpoint of each interval as the raw score
and use formula 19.6 to calculate the standard deviation:
s 2
fxx
n1
Formula 19.6
Table 19.11 shows the procedure for calculating the standard deviation for the
grouped data in table 19.4. We know from table 19.6 that x 45 for the data
in table 19.4.