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

114 CHAPTER 4 | Variability
F I G U R E 4.5
The frequency distribution
histogram for a sample of
n 5 8 scores. The sample
mean is M 5 6.5. The smallest
distance from the mean
is 0.5 points, and the largest
distance from the mean
is 4.5 points. The standard
distance (standard deviation)
should be between 0.5 and
4.5 points, or about 2.5.
f
3
2
1
M = 6.5
1 2 3 4 5 6 7 8 9 10 11
1/
2
4.5
X
We begin the calculations by finding the value of SS for this sample. Because the mean
is not a whole number (M 5 6.5), the computational formula is easier to use. The scores,
and the squared scores, needed for this formula are shown in the following table.
Scores
X
Squared Scores
X 2
4 16
6 36
5 25
11 121
7 49
9 81
7 49
3 9
SX 5 52 SX 2 5 386
Using the two sums,
SS 5SX 2 2 (SX)2
n
5 386 2 s52d2
8
5 386 2 338
5 48
The sum of squared deviations for this sample is SS 5 48. Continuing the calculations,
sample variance 5 s 2 5
SS
n 2 1 5 48
8 2 1 5 6.86
Finally, the standard deviation is
s 5 Ïs 2 5 Ï6.86 5 2.62
Note that the value we obtained is in excellent agreement with our preliminary prediction
(see Figure 4.5).
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