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

666 APPENDIX C | Solutions for Odd-Numbered Problems in the Text
3. A standard deviation of zero indicates there is no variability. In this case, all of the scores in the sample have exactly
the same value.
5. Sample A has SS = 10. The definitional formula works well. Sample B has SS = 13. The computational formula is
better when the mean is not a whole number.
7. SS = 28, variance is 4, and the standard deviation is 2.
9. a. The mean is 4, SS = 20, σ 2 = 4, and σ = 2.
b. SS = 20, s 2 = 5, and s = Ï5 = 2.24.
11. a. Figure C2
3
M 5 6
f
2
1
0 1
X
2 6543
987
10 11
b. The mean is 36
6 = 6. The three scores of X = 5
are one point from the mean. The score X = 0 is
farthest from the mean (6 points). The standard
deviation should be between 1 and 6 points, probably
around 3.5.
c. SS = 80, s 2 = 16, s = 4, which agrees with the
estimate.
13. SS = 36, s 2 = 9, and s = 3.
15. a. The original mean is M = 64 and the standard
deviation is s = 13.
b. The original mean is M = 16 and the standard
deviation is s = 6.
17. a. The simplified scores had M = 1.5, SS = 28, and
s = 2.
b. The original scores had M = 0.75 and s = 1.
19. a. The range is either 14 or 15, and the standard
deviation is s = 5.
b. After spreading out the two scores in the
middle, the range is still 14 or 15 but the
standard deviation is now s = 7.
c. The two distributions are the same according to
the range. The range is completely determined by
the two extreme scores and is insensitive to the
variability of the rest of the scores. The
second distribution has more variability
according to the standard deviation, which
measures variability for the complete set.
21. a. For the older adults, the mean is M = 5.47,
SS = 65.73, s 2 = 4.70 and s = 2.17. For the
younger adults, the mean is M = 7.27,
SS = 18.93, s 2 = 1.35, and s = 1.16.
b. The younger adults had a higher average and were
much less variable.
23. a. With σ = 20, X = 70 is not an extreme score. It is
located above the mean by a distance of only one
standard deviation.
b. With σ = 5, X = 70 is an extreme score. It is
located above the mean by a distance equal to four
times the standard deviation.
CHAPTER 5
z-Scores
1. The sign of the z-score tells whether the location is
above (+) or below (–) the mean, and the magnitude
tells the distance from the mean in terms of the number
of standard deviations.
3. a. above the mean by 40 points
b. above the mean by 10 points
c. below the mean by 20 points
d. below the mean by 5 points