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

SECTION 4.6 | More about Variance and Standard Deviation 119
2. A researcher selects all the possible samples with n 5 3 scores from a population
and computes the sample variance, dividing by n – 1, for each sample. If the
population variance is s 2 5 6, then what is the average value for all of the sample
variances?
a. 6
b. greater than 6
c. less than 6
d. impossible to determine
3. Which of the following is an example of an unbiased statistic.
a. the sample mean
b. the sample variance (dividing by n 2 1)
c. both the sample mean and the sample variance (dividing by n 2 1)
d. neither the sample mean nor the sample variance (dividing by n 2 1)
ANSWERS
1. C, 2. A, 3. C
4.6 More about Variance and Standard Deviation
LEARNING OBJECTIVES
13. Describe how the mean and standard deviation are represented in a frequency
distribution graph of a population or sample distribution.
14. Explain how the mean and standard deviation are affected when a constant is added
to every score or when every score is multiplied by a constant.
15. Describe how the mean and standard deviation are reported in research journals.
16. Describe the appearance of a distribution based on the values for the mean and
standard deviation.
17. Explain how patterns in sample data are affected by sample variance.
■ Presenting the Mean and Standard Deviation
in a Frequency Distribution Graph
In frequency distribution graphs, we identify the position of the mean by drawing a
vertical line and labeling it with m or M. Because the standard deviation measures
distance from the mean, it is represented by a line or an arrow drawn from the mean
outward for a distance equal to the standard deviation and labeled with a s or an s.
Figure 4.6(a) shows an example of a population distribution with a mean of m 5 80 and
a standard deviation of s 5 8, and Figure 4.6(b) shows the frequency distribution for a
sample with a mean of M 5 16 and a standard deviation of s 5 2. For rough sketches,
you can identify the mean with a vertical line in the middle of the distribution. The
standard deviation line should extend approximately halfway from the mean to the
most extreme score. [Note: In Figure 4.6(a) we show the standard deviation as a line
to the right of the mean. You should realize that we could have drawn the line pointing