Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 7.2 | The Distribution of Sample Means for any Population and any Sample Size 205
(a) Original population of IQ scores.
s 5 15
m 5 100
(b) A sample of n 5 25 IQ scores.
s 5 11.5
80 90 100 110 120 130
M 5 101.2
(c) The distribution of sample means. Sample means for
all the possible random samples of n 5 25 IQ scores.
FIGURE 7.4
Three distributions. Part (a)
shows the population of
IQ scores. Part (b) shows a
sample of n = 25 IQ scores.
Part (c) shows the distribution
of sample means for samples
of n = 25 IQ scores. Note
that the mean for the sample
in part (b) is one of the thousands
of sample means in the
distribution shown in part (c).
m 5 100
s M 5 3
μ = 100 and a standard deviation (standard error) of σ M
= 15 = 3. This distribution,
shown in Figure 7.4(c), also has its own shape, mean, and standard
Ï25
deviation.
Note that the scores for the sample (Figure 7.4(b)) were taken from the original population
(Figure 7.4(a)) and that the mean for the sample is one of the values contained in the distribution
of sample means (Figure 7.4(c)). Thus, the three distributions are all connected,
but they are all distinct.