CHAPTER 2 │ DESCRIPTIVE STATISTICS 89
8.
10.
11.
90 CHAPTER 2 │ DESCRIPTIVE STATISTICS
14. x=not possible
median = not possible
mode = “Approved”
The mean and median cannot be found because the data are at the nominal level of measurement.
15.
Midpoint,
x
Frequency,
f
x · f
10 2 20
16.
x f x · f
0 13 0
1 9 9
CHAPTER 2 │ DESCRIPTIVE STATISTICS 91
17.
Source Score, x Weight, w x · w
Test 1 78 0.15 11.7
∑
()
82.1xw⋅=
∑
()
82.1 82.1
1
xw
xw
∑⋅
===
∑
18.
Source Score, x Weight, w x · w
∑
()
88.8xw⋅=
∑
()
88.8 88.8
1
xw
xw
∑⋅
===
∑
19. Skewed 20. Skewed 21. Skewed left 22. Skewed right
23. Median, because the mean is to the left of the median in a skewed left distribution.
92 CHAPTER 2 │ DESCRIPTIVE STATISTICS
27. 96 6.9
14
x
N
µ∑
==≈
x −
x
µ
(
)
2
xµ−
4 –2.9 8.41
2 –4.9 24.01
9 2.1 4.41
12 5.1 26.01
15 8.1 65.61
3 –3.9 15.21
96x=
∑
()
0xµ−≈
∑
()
2295.74xµ−=
∑
()
2295.74 4.6
14
x
N
µ
σ∑−
==≈
28. 612 68
9
x
N
µ∑
===
x −
x
µ
(
)
2
xµ−
55 –13 169
89 21 441
73 5 25
CHAPTER 2 │ DESCRIPTIVE STATISTICS 93
29. 36,801 2453.4
15
x
xn
∑
== =
x −
x
x
(
)
2
x−
2445 –8.4 70.56
2940 486.6 236,779.56
2399 –54.4 2959.36
1960 –493.4 243,443.56
2710 256.6 65,843.56
2761 307.6 94,617.76
2377 –76.4 5836.96
36,801x=
∑
()
0xx−=
∑
()
21,311,783.6xx−=
∑
30. 416,659 52,082.4
8
x
xn
∑
== ≈
x −
x
x
(
)
2
x
x−
49,632 –2450.4 6,004,460.16
54,619 2536.6 6,434,339.56
31. 99.7% of the distribution lies within 3 standard deviations of the mean.
()( )
3 49 3 2.50 41.5µσ−=− =
94 CHAPTER 2 │ DESCRIPTIVE STATISTICS
32.
()()()
()
()
46.75, 52.25 49.50 1 2.75 , 49.50 1 2.75 , xsxs→− + →−+
68% of the cable rates lie between $46.75 and $52.25.
35.
x f xf
x
x−
(
)
2
x−
(
)
2
x
xf−
0 1 0 –2.5 6.25 6.25
1 8 8 –1.5 2.25 18.00
2 13 26 –0.5 0.25 3.25
36.
x f xf
x
x−
(
)
2
x
x−
(
)
2
x
xf−
0 4 0 –2.4 5.76 23.04
1 5 5 –1.4 1.96 9.80
2 2 4 –0.4 0.16 0.32
3 9 27 0.6 0.36 3.24
CHAPTER 2 │ DESCRIPTIVE STATISTICS 95
37.
Min = 42, 147.5Q=, 253Q=, 354Q=, Max = 60
41.
IQR = 31
QQ− = 31.5 – 27.0 = 4.5
The distribution is symmetric.
96 CHAPTER 2 │ DESCRIPTIVE STATISTICS
47. 18,000 11,830 2.60
2370
z−
== 48.
11,300 11,830 0.22
2370
z−
==−
CHAPTER 2 QUIZ SOLUTIONS
1a. Max Min 157 101
Class width = 11.2 12
Number of classes 5
−−
==⇒
Class Midpoint Class
boundaries
Frequency, f Relative
frequency
Cumulative
frequency
101-112 106.5 100.5-112.5 3 0.12 3
113-124 118.5 112.5-124.5 11 0.44 14
b. Frequency histogram and polygon c. Relative frequency histogram
f.
Min = 101,
=
, 2123Q=, 3131.5Q=, Max = 157
CHAPTER 2 │ DESCRIPTIVE STATISTICS 97
g.
2.
Midpoint,
x
Frequency,
f xf
x
x−
(
)
2
x
x−
(
)
2
x
xf−
106.5 3 319.5 –18.7 349.69 1049.07
118.5 11 1303.5 –6.7 44.89 493.79
130.5 7 913.5 5.3 28.09 196.63
3a.
Category Frequency Relative frequency Degrees
Clothing 10.6 0.1330
48°
Footwear 17.2 0.2158
78°
98 CHAPTER 2 │ DESCRIPTIVE STATISTICS
b.
b. Range = Max – Min = 1019 – 444 = 575
x
x
x−
(
)
2
x−
774 22.4 501.76
446 –305.6 93,391.36
1019 267.4 71,502.76
795 43.4 1883.56
()
2
2336,945.88 48,135.1
17
xx
sn
∑−
== ≈
−
()
2
336,945.88 219.4
17
xx
sn
∑−
== ≈
−
CHAPTER 2 │ DESCRIPTIVE STATISTICS 99
d. 122,000 :x= 122,000 155,000 2.2
15, 000
x
zµ
σ
−−
== =−⇒
unusual price
CUMULATIVE REVIEW FOR CHAPTERS 1 AND 2
1. Systematic sampling. A bias may enter this study if the machine makes a consistent error.
2. Simple Random Sampling. A bias of this type of study is that the researchers did not include
people without telephones.
5. 19% is a statistic because it is describing a proportion within a sample of 100 adults.
6a. 83,500, $1500xs==
()()
80,500 86,500 83,500 2 1500=± ⇒2 standard deviations away form the mean.
Approximately 95% of the electrical engineers will have salaries between (80,500 86,500).
b. 40(0.95) = 38
100 CHAPTER 2 │ DESCRIPTIVE STATISTICS
1500
σ
The salaries of $90,500 and $79,750 are unusual.
7. Population: Collection of the career interests of all college and university students
Sample: Collection of the career interests of the 195 college and university students whose career
counselors were surveyed
8. Population: Collection of the life spans of all people
Sample: Collection of the life spans of the 232,606 people in the study
13.
Min = 0, 12Q=, 212.5Q=, 339Q=, Max = 136
CHAPTER 2 │ DESCRIPTIVE STATISTICS 101
14.
Source Score, x Weight, w x · w
Test 1 85 0.15 12.75
Test 2 92 0.15 13.80
15a. 49.4 5.49
9
x=≈
mode = none
Both the mean and median accurately describe a typical American alligator tail length.
(Answers will vary.)
b. Range – Max – Min – 7.5 – 3.4 = 4.1
x
x
x−
(
)
2
x−
3.4 –2.09 4.3681
3.9 –1.59 2.5281
4.2 –1.29 1.6641
16a. The number of deaths due to heart disease for women will continue to decrease.
b. The study was only conducted over the past 5 years and deaths may not decrease in the next
year.
102 CHAPTER 2 │ DESCRIPTIVE STATISTICS
17. Max Min 65 0
Class width = 8.125 9
Number of classes 8
−−
==⇒
Class
limits
Midpoint Class
boundaries
Frequency Relative
frequency
Cumulative
frequency
0-8 4 –0.5-8.5 8 0.27 8
9-17 13 8.5-17.5 5 0.17 13
18-26 22 17.5-26.5 7 0.23 20
n=
18. The distribution is skewed right.
19.