Russel-Research-Method-in-Anthropology

Univariate Analysis 565
TABLE 19.4
Frequency Table of the Grouped Variable AGE
Count Cum. Count Variable AGE
6 6 20–29
6 12 30–39
5 17 40–49
8 25 50–59
5 30 60
PS L i nC
f
Formula 19.1
where:
PS is the percentile score you want to calculate;
L is the true lower limit of the interval in which the percentile score lies;
n is the case number that represents the percentile score;
C is the cumulative frequency of the cases up to the interval before the one in
which the percentile score lies;
i is the interval size; and
f is the count, or frequency, of the interval in which the median lies.
In applying formula 19.1 to the data in table 19.4, the first thing to do is
calculate n. There are 30 cases and we are looking for the score at the 50th
percentile (the median), so n is (30)(.50) 15. We are looking, in other
words, for a number above which there are 15 cases and below which there
are 15 cases. Looking at the data in table 19.4, we see that there are 12 cases
up to 39 years of age and 17 cases up to 49 years of age. So, C is 12, and the
median case lies somewhere in the 40–49 range.
The true lower limit, L, of this interval is 39.5 (midway between 39 and 40,
the boundary of the two groups), and the interval, i, is 10 years. Putting all
this into the formula, we get:
PS 39.5.10 1512
5
39.510(.6) 45.5
So, the median age for the grouped data on 30 people is 45.5 years. Notice
that: (1) The median for the ungrouped data on AGE in table 19.3b is 46.5, so
in grouping the data we lose some accuracy in our calculation; and (2) None