Russel-Research-Method-in-Anthropology

564 Chapter 19
vations on a variable, the median score is (n 1)/2, where n is the number of
cases in a distribution and the scores are arranged in order.
Suppose we ask nine people to tell us how many brothers and sisters they
have, and we get the following answers:
0 0 1 1 1 1 2 2 3
The median observation is 1 because it is the middle score—there are four
scores on either side of it, (n 1)/2 5, and we see that the median is the
fifth case in the series, once the data are arranged in order.
Often as not, of course, as with the data on those 30 respondents from the
green survey shown in table 19.2, you’ll have an even number of cases. Then
the median is the average of n/2 and (n/2 1), or the midpoint between the
two middle observations, once the data are arranged in order. I asked 16
undergraduate students ‘‘How long do you think you’ll live?’’ Here are the
responses:
70 73 75 75 79 80 80 83 85 86 86 87 87 90 95 96
n/2 8 and n/2 1 9, so the median is 84, midway between the two
middle observations, 83 and 85. (By the way, if the two middle observations
had been, say, 83, then the midpoint between them would be 83.)
The Median of Grouped Data
A lot of data are reported in intervals, or groups. For example, some people
are uncomfortable with a straightforward question like ‘‘How much money do
you make?’’ so researchers often ask something like:
Now we’d like to get an idea of about how much you earn each year. Do you
earn:
(1) less than $10,000 per year?
(2) $10,000 or more but less than $20,000 per year?
(3) $20,000 or more but less than $30,000 per year?
(4) $30,000 or more but less than $40,000 per year?
(5) $40,000 or more but less than $50,000 per year?
and so on. This produces grouped data. In table 19.3b, the two middle scores
for AGE are 46 and 47, so the median is 46.5. Table 19.4 shows the data on
AGE from table 19.3b, grouped into 10-year intervals. To find the median in
grouped data, use the formula for finding any percentile score in a distribution
of grouped data: