a.
0
b.
.5
c.
1
d.
None of the other answers is correct.
100. For data skewed to the left, the skewness is
a.
between 0 and .5
b.
less than 1
c.
positive
d.
negative
101. When the data are positively skewed, the mean will usually be
a.
less than the median
b.
greater than the median
c.
less than the mode
d.
greater than the mode
102. The measure of location often used in analyzing growth rates in financial data is the
a.
arithmetic mean
b.
weighted mean
c.
geometric mean
d.
hyperbolic mean
103. The measure of central location most often reported for annual income and property value data is the
a.
median
b.
mode
c.
weighted mean
d.
aggregate mean
104. Chebyshev’s theorem requires that z be
a.
an integer
b.
greater than 1
c.
less than or equal to 3
d.
between 0 and 4
105. Chebyshev’s theorem is applicable
a.
only to large (n > 30) data sets
b.
only to data sets with no outliers
c.
only to bell-shaped data sets
d.
to any data set
106. A set of visual displays that organizes and presents information that is used to monitor the
performance of a company or organization in a manner that is easy to read, understand, and interpret is
called a
a.
stem-and-leaf display
b.
stacked bar chart
c.
data dashboard
d.
crosstabulation
PROBLEM
1. The hourly wages of a sample of eight individuals is given below.
Individual
Hourly Wage ($)
A
27
B
25
C
20
D
10
E
12
F
14
G
17
H
19
For the above sample, determine the following measures:
a.
The mean.
b.
The standard deviation.
c.
The 25th percentile.
a.
18
b.
6
c.
12.5
2. In 2012, the average age of students at UTC was 22 with a standard deviation of 3.96. In 2013, the
average age was 24 with a standard deviation of 4.08. In which year do the ages show a more
dispersed distribution? Show your complete work and support your answer.
3. For the following data
7
9
15
Compute the following measures:
a.
The mean
b.
The variance
c.
The standard deviation
d.
The coefficient of variation
e.
The 25th percentile
f.
The median
g.
The 75th percentile
4. For the following data
18
17
22
21
17
Compute the following measures:
a.
The mean
b.
The variance
c.
The standard deviation
d.
The coefficient of variation
e.
The 25th percentile
f.
The median
g.
The 75th percentile
a.
20
b.
5.75
c.
2.4
d.
11.99
e.
17.5
20
g.
22.5
5. A private research organization studying families in various countries reported the following data for
the amount of time 4-year old children spent alone with their fathers each day.
Country
Time with Dad (minutes)
Belgium
30
Canada
44
China
54
Finland
50
Germany
36
Nigeria
42
Sweden
46
United States
42
a.
11
b.
27.2
c.
5.22
d.
47.41
e.
6.5
10
g.
16
For the above sample, determine the following measures:
a.
The mean
b.
The standard deviation
c.
The mode
d.
The 75th percentile
6. The following data show the yearly salaries of football coaches at some public high schools.
High School
Salary ($1,000)
A
53
B
44
C
68
D
47
E
62
F
59
G
53
H
94
For the above sample, determine the following measures.
a.
The mean yearly salary
b.
The standard deviation
c.
The mode
d.
The median
e.
The 70th percentile
a.
60
b.
15.8
c.
53
d.
56
e.
63.8
7. The amount of time that a sample of students spends watching television per day is given below.
Student
Time (minutes)
1
40
2
28
3
71
4
48
5
49
6
35
7
40
8
57
a.
43
b.
7.56
c.
42
d.
49
a.
Compute the mean.
b.
Compute the median.
c.
Compute the standard deviation.
d.
Compute the 75th percentile.
8. The number of hours worked per week for a sample of ten students is shown below.
Student
Hours
1
20
2
0
3
18
4
16
5
22
6
40
7
8
8
6
9
30
10
40
a.
Determine the median and explain its meaning.
b.
Compute the 70th percentile and explain its meaning.
c.
What is the mode of the above data? What does it signify?
a.
19; approximately 50% of the students work at least 19 hours
b.
27.6; at least 70% of the students work less than or equal to 27.6 hours per week
c.
40; the most frequent data element
9. A researcher has obtained the number of hours worked per week during the summer for a sample of
fifteen students.
40
25
35
30
20
40
30
20
40
10
30
20
10
5
20
Using this data set, compute the
a.
median
b.
mean
c.
mode
d.
40th percentile
e.
range
f.
sample variance
g.
standard deviation
a.
46
b.
44
c.
13.5
d.
55
10. A sample of twelve families was taken. Each family was asked how many times per week they dine in
restaurants. Their responses are given below.
2
1
0
2
0
2
1
2
0
2
1
2
Using this data set, compute the
a.
mode
b.
median
c.
mean
d.
range
e.
interquartile range
f.
variance
g.
standard deviation
h.
coefficient of variation
a.
2
b.
1.5
c.
1.25
d.
2
e.
1.75
f.
0.75
g.
0.866
h.
69.28%
11. A sample of 9 mothers was taken. The mothers were asked the age of their oldest child. You are given
their responses below.
12
4
14
2
9
a.
Compute the mean.
b.
Compute the variance.
c.
Compute the standard deviation.
d.
Compute the coefficient of variation.
e.
Determine the 25th percentile.
f.
Determine the median
g.
Determine the 75th percentile.
h.
Determine the range.
a.
25
b.
25
c.
20
d.
20
e.
35
128.571
g.
11.339
12. A sample of 11 individuals shows the following monthly incomes.
Individual
Income ($)
1
1,500
2
2,000
3
2,500
4
4,000
5
4,000
6
2,500
7
2,000
8
4,000
9
3,500
10
3,000
11
43,000
a.
What would be a representative measure of central location for the above data? Explain.
b.
Determine the mode.
c.
Determine the median.
d.
Determine the 60th percentile.
e.
Drop the income of individual number 11 and compute the standard deviation for the first 10
individuals.
a.
Median, because the income of individual 11 is unusually high.
b.
4000
c.
3000
d.
3600
e.
936.90
13. Suppose annual salaries for sales associates from a particular store have a mean of $32,500 and a
standard deviation of $2,500.
a.
Calculate and interpret the z-score for a sales associate who makes $36,000.
b.
Use Chebyshev’s theorem to calculate the percentage of sales associates with salaries between
$26,250 and $38,750.
c.
Suppose that the distribution of annual salaries for sales associates at this store is bell-shaped.
Use the empirical rule to calculate the percentage of sales associates with salaries between
$27,500 and $37,500.
d.
Use the empirical rule to determine the percentage of sales associates with salaries less than
$27,500.
e.
Still suppose that the distribution of annual salaries for sales associates at this store is
a.
7.56
b.
17.78
c.
4.22
d.
55.8
e.
3.5
7.0
g.
11.5
h.
12
bell-shaped. A sales associate makes $42,000. Should this salary be considered an outlier?
Explain.
14. Provide a five-number summary for the follow data.
115
191
153
194
236
184
216
185
183
202
15. The following observations are given for two variables.
y
x
5
2
8
12
18
3
20
6
22
11
30
19
10
18
7
9
a.
Compute and interpret the sample covariance for the above data.
b.
Compute and interpret the sample correlation coefficient.
19.286 (rounded). Since the covariance is positive, it indicates a positive relationship between x
and y.
b.
0.345. There is a positive relationship between x and y. The relationship is not very strong.
16. The following data represent the daily demand (y in thousands of units) and the unit price (x in dollars)
for a product.
b.
84%
95%
d.
2.5%
3.8.
Daily Demand (y)
Unit Price (x)
47
1
39
3
35
5
44
3
34
6
20
8
15
16
30
6
a.
Compute and interpret the sample covariance for the above data.
b.
Compute and interpret the sample correlation coefficient.
17. Compute the weighted mean for the following data.
xi
Weight (wi)
9
10
8
12
5
4
3
5
2
3
18. Compute the weighted mean for the following data.
xi
Weight (wi)
19
12
17
30
14
28
13
10
18
10
19. Paul, a freshman at a local college just completed 15 credit hours. His grade report is presented below.
Course
Credit Hours
Grades
Calculus
5
C
Biology
4
A
English
3
D
Music
2
B
P.E.
1
A
The local university uses a 4 point grading system, i.e., A = 4, B = 3, C = 2, D = 1, F = 0. Compute
Paul’s semester grade point average.
20. Consider the data in the following frequency distribution. Assume the data represent a population.
Class
Frequency
2 − 6
2
7 − 11
3
12 − 16
4
17 − 21
1
For the above data, compute the following.
a.
The mean
b.
The variance
c.
The standard deviation
a.
11
b.
21
c.
4.58
21. The following frequency distribution shows the ACT scores of a sample of students:
Score
Frequency
14 − 18
2
19 − 23
5
24 − 28
12
29 − 33
1
For the above data, compute the following.
a.
The mean
b.
The standard deviation
a.
24
b.
3.77
22. The following is a frequency distribution of grades for a statistics examination.
Examination Grade
Frequency
40 − 49
3
50 − 59
5
60 − 69
11
70 − 79
22
80 − 89
15
90 − 99
6
Treating these data as a sample, compute the following:
a.
The mean
b.
The standard deviation
c.
The variance
d.
The coefficient of variation
23. The starting salaries of a sample of community college graduates are given below.
Starting Salary ($1000s)
Frequency
10 − 14
2
15 − 19
3
20 − 24
5
25 − 29
7
30 − 34
2
35 − 39
1
a.
Compute the mean.
b.
Compute the variance.
c.
Compute the standard deviation.
d.
Compute the coefficient of variation.
a.
23.7
b.
42.83
c.
6.54
d.
27.59
24. The following frequency distribution shows the time (in minutes) that a sample of students uses the
computer terminals per day.
Time (minutes)
Frequency
20 − 39
2
40 − 59
4
60 − 79
6
a.
74.016
b.
12.601
c.
158.778
d.
17.02%
80 − 99
4
100 − 119
2
a.
Compute the mean.
b.
Compute the variance.
c.
Compute the standard deviation.
d.
Compute the coefficient of variation.
25. A sample of charge accounts at a local drug store revealed the following frequency distribution of
unpaid balances.
Unpaid Balance ($)
Frequency
10 − 29
5
30 − 49
10
50 − 69
6
70 − 89
9
90 − 109
20
a.
Determine the mean unpaid balance.
b.
Determine the standard deviation.
c.
Compute the coefficient of variation.
a.
71.1
b.
28.88
c.
40.62%
26. The following is a frequency distribution for the ages of a sample of employees at a local company.
Age
Frequency
30 − 39
2
40 − 49
3
50 − 59
7
60 − 69
5
70 − 79
1
a.
Determine the average age for the sample.
b.
Compute the variance.
c.
Compute the standard deviation.
d.
Compute the coefficient of variation.
a.
69.5
b.
564.54
c.
23.76
d.
34.19%
27. Del Michaels had a successful morning, or so he thinks, selling 1300 surplus notebook computers over
the telephone to three commercial customers. The three customers were not equally skillful at
negotiating a low unit price. Customer A bought 600 computers for $1252 each, B bought 300 units
at $1310 each, and C bought 400 at $1375 each.
a. What is the average unit price at which Del sold the 1300 computers?
b. Del’s manager told Del he expected him to sell, by the end of the day, a total of 2500 surplus
computers at an average price of $1312 each. What is the average unit price at which Del must
sell the remaining 1200 computers?
28. Missy Walters owns a mail-order business specializing in baby clothes. She is considering offering
her customers a discount on shipping charges based on the dollar-amount of the mail order. Before
Missy decides the discount policy, she needs a better understanding of the dollar-amount distribution
of the mail orders she receives. Missy had an assistant randomly select 50 recent orders and record
the value, to the nearest dollar, of each order as shown below.
136
281
226
123
178
445
231
389
196
175
211
162
212
241
182
290
434
167
246
338
194
242
368
258
323
196
183
209
198
212
277
348
173
409
264
237
490
222
472
248
231
154
166
214
311
141
159
362
189
260
a. Determine the mean, median, and mode for this data set.
b. Determine the 80th percentile.
c. Determine the first quartile.
d. Determine the range and interquartile range.
e. Determine the sample variance, sample standard deviation, and coefficient of variation.
f. Determine the z–scores for the minimum and maximum values in the data set.
29. Ron Butler, a custom home builder, is looking over the expenses he incurred for a house he just
completed constructing. For the purpose of pricing future construction projects, he would like to
know the average wage ($/hour) he paid the workers he employed. Listed below are the categories of
worker he employed, along with their respective wage and total hours worked. What is the average
wage ($/hour) he paid the workers?
Worker
Wage ($/hr)
Total Hours
Carpenter
21.60
520
Electrician
28.72
230
Laborer
11.80
410
Painter
19.75
270
Plumber
24.16
160
30. The manager of Hudson Auto Repair has recorded the following frequency distribution for the cost of
new parts used in doing an engine tune-up in a sample of 50 tune-ups.
Parts Cost ($)
Frequency
50-59
2
60-69
13
70-79
17
80-89
7
90-99
6
100-109
5
Compute the sample mean, variance, and standard deviation.
31. Given below is a sample of 70 monthly rents for one-bedroom apartments presented as grouped data in
the form of a frequency distribution. Compute the sample mean, variance, and standard deviation.
Rent ($)
Frequency
Rent ($)
Frequency
420-439
8
520-539
4
440-459
17
540-559
2
460-479
12
560-579
4
480-499
8
580-599
2
500-519
7
600-619
6
32. Angela Lopez, a golf instructor, is interested in investigating the relationship between a golfer’s
average driving distance and 18-hole score. She recently observed the performance of six golfers
during one round of a tournament and measured, as accurately as possible, the distances (yards) of
their drives and noted their final scores. She then computed each golfer’s average drive distance for
18 holes. The results of her sample are shown below.
Golfer
Avg. Drive
(yards)
18-Hole
Score
1
277.6
69
2
259.5
71
3
269.1
70
4
267.0
70
5
255.6
71
6
272.9
69
Compute and interpret both the sample covariance and the sample correlation coefficient.
33. Reed Auto periodically has a special week-long sale. As part of the advertising campaign Reed runs
one or more television commercials during the weekend preceding the sale. Data from a sample of 5
previous sales are shown below.
Week
TV Ads
Cars Sold
1
1
14
2
3
24
3
2
18
4
1
17
5
3
27
Compute and interpret both the sample covariance and the sample correlation coefficient.