Russel-Research-Method-in-Anthropology

566 Chapter 19
of the respondents in table 19.3b actually reported a median age of 45.5 or
46.5.
I’ve given you this grand tour of the median as a specific percentile score
because I want you to understand the conceptual basis for this statistic. I’m
going to do the same thing for all the statistical procedures I introduce here
and in the next two chapters. You only need to work through these detailed
examples once. When you understand the concepts behind the median, the
standard deviation, z-scores, chi-square, t-tests, and regression, you need
never again calculate these statistics by hand. Once you understand a statistic,
you can do all the calculations by computer.
In fact, even for small data sets, it’s best to use a computer to handle statistical
chores. It’s not just easier to do—it’s more accurate. You’re less likely to
make mistakes in recording data on a computer and when you do make mistakes
(I make them all the time), it’s easier to find and fix them. Just think of
how easy it is to find spelling errors in a document when you use a word processor.
It’s the same with checking and correcting mistakes in statistical analysis.
Central Tendency: The Mean
The arithmetic mean, or the average, is the sum of the individual scores in
a distribution, divided by the number of scores. The formula for calculating
the mean is:
x x /n Formula 19.2
where x (read: x-bar) is the mean, x means ‘‘sum all the values of x’’ and n
is the number of values of x. To calculate the mean, or average age of the 30
respondents whose data are shown in table 19.2, we add up the 30 ages and
divide by 30. The mean age of these 30 respondents is 45.033 years. (We use
x when we refer to the mean of a sample of data; we use the Greek letter
when we refer to the mean of an entire population.)
The formula for calculating the mean of a frequency distribution is:
x fx / n Formula 19.3
where fx / n is the sum of the attributes of the variable, times their frequencies.
Table 19.5 shows the calculation of the mean age for the frequency distribution
shown in table 19.3b.