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

128 CHAPTER 4 | Variability
DEMONSTRATION 4.1
COMPUTING MEASURES OF VARIABILITY
For the following sample data, compute the variance and standard deviation. The scores are:
10, 7, 6, 10, 6, 15
STEP 1
Compute SS, the sum of squared deviations
For this sample, n = 6 and
We will use the computational formula.
SX 5 10 1 7 1 6 1 10 1 6 1 15 5 54
SX 2 5 10 2 1 7 2 1 6 2 1 10 2 1 6 2 1 15 2 5 546
SS 5SX 2 2 sSXd2
N
5 546 2 486
560
s54d2
5 546 2
6
STEP 2
STEP 3
Compute the sample variance
freedom, df 5 n 2 1.
For sample variance, SS is divided by the degrees of
s 2 5
Compute the sample standard deviation
of the variance.
SS
n 2 1 5 60 5 5 12
Standard deviation is simply the square root
s 5 Ï12 5 3.46
PROBLEMS
1. In words, explain what is measured by SS, variance,
and standard deviation.
2. Is it possible to obtain a negative value for the variance
or the standard deviation?
3. Describe the scores in a sample that has a standard
deviation of zero.
4. There are two different formulas or methods that can
be used to calculate SS.
a. Under what circumstances is the definitional
formula easy to use?
b. Under what circumstances is the computational
formula preferred?
5. Calculate the mean and SS (sum of squared deviations)
for each of the following samples. Based on
the value for the mean, you should be able to decide
which SS formula is better to use.
Sample A: 1, 3, 4, 0
Sample B: 2, 5, 0, 3
6. Calculate SS, variance, and standard deviation for the
following population of N 5 5 scores: 2, 13, 4, 10, 6.
(Note: The definitional formula works well with these
scores.)
7. Calculate SS, variance, and standard deviation for the
following population of N 5 7 scores: 8, 1, 4, 3, 5, 3,
4. (Note: The definitional formula works well with
these scores.)
8. For the following population of N 5 6 scores:
3, 1, 4, 3, 3, 4
a. Sketch a histogram showing the population
distribution.
b. Locate the value of the population mean in your
sketch, and make an estimate of the standard
deviation (as done in Example 4.2).
c. Compute SS, variance, and standard deviation for
the population. (How well does your estimate compare
with the actual value of s?)