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Witte & Witte, 9e
Chapter 4 Exercises
Page 1 of 7 Pages
Chapter 4 Describing Variability
Exercise 1
1. The mean height of female students at a community college is 63.8 inches with a
standard deviation of 2.6 inches.
a. The majority of female student heights fall between what two values?
b. A small minority of female student heights are less than what value?
c. A small minority of female student heights are greater than what value?
Answers:
a. 61.2” and 66.4”
b. 58.6”
c. 69.0”
2. The mean height of male students at a community college is 69.2 inches with a
standard deviation of 2.6 inches.
a. The majority of male student heights fall between what two values?
b. A small minority of male student heights are less than what value?
c. A small minority of male student heights are greater than what value?
Answers:
a. 66.6” and 71.8”
b. 64.0”
c. 74.4”
Exercise 2
1. Berta samples the IQ scores of 100 third graders. She calculates the standard
deviation and obtains a result of –14.5. Based on this result, we can say with
certainty that
a. The sample included many extremely low IQ scores.
b. The distribution of IQ scores was negatively skewed.
c. Berta made a mistake when she calculated the standard deviation.
d. The distribution had a very small range.
Answer: c
Witte & Witte, 9e
Chapter 4 Exercises
Page 2 of 7 Pages
2. A math achievement test was administered to students in two elementary schools.
A summary of the results is given below.
School A: Mean = 50, Standard Deviation = 10
School B: Mean = 60, Standard Deviation = 10
Based on these results, we can say with certainty that
a. The two distributions have the same range.
b. The two distributions have the same variance.
c. The scores in School B are more variable than the scores in School A.
d. All the School A scores are between 40 and 60, and all the School B scores
are between 50 and 70.
Answer: b
3. A reading achievement test was administered to students in two elementary
schools. A summary of the results is given below.
School A: Mean = 45, Variance = 64
School B: Mean = 45, Variance = 81
Based on these results, we can say with certainty that
a. More students scored above the mean in School B than in School A.
b. All the School A scores are between 37 and 53, and all the School B
scores are between 36 and 54.
c. The two distributions have the same range.
d. The two distributions have different standard deviations.
Answer: d
Exercise 3
Brett Favre was a quarterback for the Green Bay Packers football team from 1992
through 2007. The table below displays his passing touchdowns and interceptions while
he played for the Packers. Source:
http://www.nfl.com/players/brettfavre/profile?id=FAV540222
Year
1992
1993
1994
1995
1996
Passing
TDs
18
19
33
38
39
Interceptions
13
24
14
13
13
Witte & Witte, 9e
Chapter 4 Exercises
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
Page 3 of 7 Pages
35
31
22
20
32
27
32
30
20
18
28
Mean =
1.
16
23
23
16
15
16
21
17
29
18
15
27.63
17.88
Viewing these data as a population, use the computation formula to
calculate the sum of squares for Passing TDs.
Year
X (Passing TDs)
1992
18
1993
19
1994
33
1995
38
1996
39
1997
35
1998
31
1999
22
2000
20
2001
32
2002
27
2003
32
2004
30
2005
20
2006
18
2007
28
442
Answer: SS = 783.75
X2
324
361
1089
1444
1521
1225
961
484
400
1024
729
1024
900
400
324
784
12994
Witte & Witte, 9e
Chapter 4 Exercises
Page 4 of 7 Pages
2. Calculate the variance of the Passing TD distribution.
Answer:  2 = 48.98
3.Calculate the standard deviation of the Passing TD distribution.
Answer: ∑ = 6.999
4.Calculate the range of the Passing TDs.
Answer: Range = 39-18 = 21
Exercise 4
Dr. Felicity Bark carried out a research study to see if female and male dog owners
differed with respect to the time that they spent talking to their dogs. She randomly
selected 15 female dog owners and 10 male dog owners from a pool of volunteers. Each
owner-dog pair was placed, one at a time, in the same room for 4 minutes. The ownerdog dyads were videotaped and the total time that each owner spent talking to his/her dog
was recorded. Those data are shown below.
Female Owner
Male Owner
Time (in seconds)
106
37
144
217
211
240
2
111
204
57
79
8
3
58
73
Time (in seconds)
67
50
62
23
11
41
28
80
2
113
Witte & Witte, 9e
Chapter 4 Exercises
Page 5 of 7 Pages
1. What symbol should be used for the variances of these two distributions?
Answer: s2
2. What symbol should be used for the standard deviation of these two
distributions?
Answer: s
3. Using the data for female owners, calculate the SS (using computation
formula), and also calculate the variance, standard deviation, range, and
interquartile range.
Answers:
X (Seconds)
106
37
144
217
211
240
2
111
204
57
79
8
3
58
73
Sum =
1550
n=
15
Mean =
103.33
Answers:
SS = 94,581.34
X2
11236
1369
20736
47089
44521
57600
4
12321
41616
3249
6241
64
9
3364
5329
254748
Witte & Witte, 9e
Chapter 4 Exercises
Page 6 of 7 Pages
s2 = 94,581.34 ÷ (15 – 1) = 6,755.81
s = = 82.19
Range = 240 – 2 = 238
3rd Quartile = 204, 1st Quartile = 37, IQR = 204-37 = 167
4. Using the data for male owners, calculate the SS(using computation
formula), and also calculate the variance, standard deviation, range, and
interquartile range.
Answers:
(477) 2
SS = 33121 –
= 10,368.1
10
s2 =
10,368.1
= 1,152.01
10  1
s = = 33.94
Range = 113-1 = 111
3rd Quartile = 67, 1st Quartile = 23, IQR = 67-23 = 44
5. Which distribution is more variable, female dog owners or male dog
owners?
Answer: Female dog owners. It is best to base your answer to this question on the
standard deviation (or variance). The standard deviation of the females’ distribution is
larger than the standard deviation of the males’ distribution.
6. If the sample female owner data are to be used to estimate the population
variance for all female dog owners, the degrees of freedom for the
estimate equals __.
Answer: df = n – 1 = 15 – 1 = 14
7. If the sample male owner data are to be used to estimate the population
variance for male owners, the degrees of freedom for the estimate would
be equal to ___.
Witte & Witte, 9e
Chapter 4 Exercises
Answer: df = n – 1 = 10 – 1 =
Page 7 of 7 Pages