Download EXERCISES ON UNIVARIATE DESCRIPTIVE ANALYSIS (FIRST

EXERCISES ON UNIVARIATE DESCRIPTIVE ANALYSIS
(FIRST PART OF THE COURSE)
1. The following are the responses of 20 students from a statistics class who were asked to evaluate their
instructor. The students were asked to choose one of five answers: Excellent (E), Above average (AA),
Average (A), Below average (B) and Poor (P).
AA
E
E






B
AA
A
A
B
B
A
E
P
E
AA
AA
AA
E
E
P
B
Classify the variable under study (qualitative or quantitative).
Prepare a frequency distribution table.
Calculate the relative frequencies and percentages for all categories.
What percentage of these students ranked this instructor as excellent or above average?
Draw a bar graph for the percentage distribution.
Compute the possible measures of central tendency.
2. The following data give the numbers of computer keyboards assembled at the Twentieth Century
Electronics Company for a sample of 25 days.




45
52
48
41
56
46
44
42
48
53
51
53
48
46
43
52
50
54
47
44
47
50
49
48
51
Construct a frequency distribution table. Take the classes as 41-44, 45-48, 49-52, 53-56.
Calculate the percentage distribution, using the classes. What percentage of days corresponds to
the numbers of computer keyboards assembled between 45 and 48?
Calculate the cumulative percentage distribution. What percentage of days corresponds to the
numbers of computer keyboards assembled between 41 and 48?
Construct a histogram for the percentage distribution.
3. The following table gives the frequency distribution of the amounts of telephone bills for October 1999
for a sample of 50 families
Amount of Telephone Bill
(dollars)
20 -| 40
40 -| 60
60 -| 80
80 -| 100
100 -| 120



Number of Families
8
13
17
9
3
Classify the variable under study.
How many families in this sample had a bill of $80 or less? What is the corresponding percentage?
Compute the mode.
4. The following table gives the average numbers of hours spent annually in gridlock on the roads by
motorists in 20 U.S. cities
City
Hours
Los Angeles
Washington
Seattle-Everett
Atlanta
Boston
Detroit
San Francisco
Houston
Dallas
Miami-Hialeah
Austin, TX
Portland-Vancouver
St. Louis
Indianapolis
San Bernardino
Baltimore
Nashville
San Jose, CA
Denver
Chicago





82
76
69
68
68
62
58
58
58
57
53
52
52
52
47
47
46
45
45
44
Defines the elements and the variable in this data set.
Construct a frequency distribution table. Take the classes as 44-50, 51-57, 58-64, 65-71, 72-78,
79-85.
Construct a histogram for the percentage distribution.
In what percentage of these cities do the motorists spend an average of 64 hours or less annually in
gridlock?
Starting from the frequency distribution table, compute the mode.
5. The following data are the salaries (in millions of dollars) of the infielders of the New York Yankees
baseball team for the 1999 season. These salaries, entered in that order, are for the players Brosius,
Degroote, Jeter, Knoblautch, Martinez, And Sojo
5.25
0.20
5.00
6.00
4.30
0.80
Compute the median and the mean. Do these data have a mode? Why or why not?
6. The following table gives the frequency distribution of the numbers of children less than 18 years of age
for 50 randomly selected families.
Numbers of children
Number of Families
0
1
2
3


Compute the mode, the median and the mean.
Compute the range, variance and standard deviation.
10
15
21
4
7. The following table gives the frequency distribution of the numbers of personal computers sold during
the past month at 40 computer stores in New York
Computers sold
Number of Store
4-12
13-21
22-30
31-39
40-48
6
9
14
7
4
Compute the mode and the mean.
8. The following data give the 1998 revenues (in millions of dollars) of the 8 automotive retailing and
service companies listed in Fortune magazine’s top 1000 U.S. companies. The data, entered in that
order, are for Republic Industries, Ryder Systems, United Auto Group, Budget Group, Avis Rent a Car,
Group 1 Automotive, Sonic Automotive and AMERCO.
17.487 5189
3045
2616
2298
1630
1604
1410
Calculate the mean and the median for these data. Do they contain an outlier? If so, drop the outlier and
recalculate the mean and the median. Which of these two summary measures changes by a large amount
when you drop the outlier? Which is the best summary measure for these data? Explain.
9. The following data give the numbers of car thefts that occurred in a city in the past 12 days
6
3
7
11
4
3
8
7
2
6
9
15
Calculate the range, variance and standard deviation.
10. The following table gives the frequency distribution of the numbers of days for which all 40 employees
of a company were absent during the last year
No. of days absent
0-2
3-5
6-8
9-11
12-14
Compute the variance and standard deviation.
Number of employees
10
14
9
4
3