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

130 CHAPTER 4 | Variability
Researchers comparing cognitive skills for younger
adults and older adults typically find greater differences
(greater diversity) in the older population
(Morse, 1993). Following are typical data showing
problem-solving scores for two groups of
participants.
Older Adults
(average age 72)
Younger Adults
(average age 31)
9 4 7 3 8 7 9 6 7 8
6 2 8 4 5 6 7 6 6 8
7 5 2 6 6 9 7 8 6 9
a. Compute the mean, variance, and standard deviation
for each group.
b. Is one group of scores noticeably more variable
(more diverse) than the other?
22. Wegesin and Stern (2004) found greater consistency
(less variability) in the memory performance scores
for younger women than for older women. The
following data represent memory scores obtained
for two women, one older and one younger, over a
series of memory trials.
a. Calculate the variance of the scores for each
woman.
b. Are the scores for the younger woman more
consistent (less variable)?
Younger
Older
8 7
6 5
6 8
7 5
8 7
7 6
8 8
8 5
23. A population has a mean of m 5 50 and a standard
deviation of s 5 20.
a. Would a score of X 5 70 be considered an extreme
value (out in the tail) in this sample?
b. If the standard deviation were s 5 5, would a
score of X 5 70 be considered an extreme value?
24. On an exam with a mean of M 5 78, you obtain a
score of X 5 84.
a. Would you prefer a standard deviation of s 5 2 or
s 5 10? (Hint: Sketch each distribution and find
the location of your score.)
b. If your score were X 5 72, would you prefer s 5 2
or s 5 10? Explain your answer.