Russel-Research-Method-in-Anthropology

176 Chapter 7
12
10
Number of Cases
8
6
4
2
0
0 100 200 300 400 500 600
PCGDP of 50 Poorest Countries
Figure 7.5. The distribution of the 50 data points for GDP in Table 7.1.
(standard deviation 37.44)—very close to the parameter of $294.16 that we’re
trying to estimate.
The problem, of course, is that in real research, we don’t get to take 15 or
50 samples. We have to make do with one. The first sample of five elements
that I took had a mean of $305.40—pretty close to the actual mean of $294.16.
But it’s very clear from table 7.3 that any one sample of five elements from
table 7.1 could be off by a lot. They range, after all, from $176.40 to $342.200.
That’s a very big spread, when the real average we’re trying to estimate is
$294.16.
Figure 7.6c shows what happens when we take 30 random samples of size
30 from the 50 elements in table 7.1. Not only is the distribution pretty normal
looking, the range of the 30 samples is between $259.88 and $321.73, the stan-
TABLE 7.3
15 Means from Samples of Size 5 Taken from the 50 Elements in Table 7.1
Mean 284.12
Standard Deviation 50.49
340.00 342.20 319.20
322.00 322.00 254.60
245.00 245.00 329.00
305.40 306.00 205.40
176.40 265.00 283.40