CHAPTER
2
Organizing and Graphing Data 1. Briefly explain the difference between ungrouped and grouped data. Give one example of each type of such data. 2. A researcher asked 30 respondents if they felt major corporations should pay their CEOs (chief executive officers) the huge salaries that are prevalent today. (N indicates no, Y represents yes, and O stands for no opinion.) N N Y
N Y N
Y Y N
O N N
N O Y
N N O
Y O O
N N N
O N N
N N Y
a. b. c. d.
Construct a frequency distribution table. Calculate the relative frequencies and percentages for all categories. What percentage of these persons is against paying huge salaries to CEOs? What percentage of these persons is either in favor of paying huge salaries to CEOs or has no opinion? e. Draw a bar graph for the relative frequency distribution. f. Draw a pie chart for the percentage distribution. 3. The following table gives the frequency distribution of the weights (in pounds) of 100 persons. Weight (in pounds) 90 to less than 110 110 to less than 130 130 to less than 150 150 to less than 170 170 to less than 190 190 to less than 210
f 8 17 21 24 19 11
a. List the class midpoints. b. Do all classes have the same width? If yes, what is that width? c. Prepare the relative frequency and percentage distribution columns.
4. The following data give the annual earnings (in thousands of dollars) of 20 families. 32.5 43.7 19.5
29.7 53.4 24.0
49.0 59.5 44.5
17.4 37.0 62.7
31.7 22.7 47.5
67.9 15.8 54.7
27.4 43.2
a. Construct a frequency distribution table. Take the classes as 10 to less than 20, 20 to less than 30, ... , and 60 to less than 70. b. Calculate the relative frequencies and percentages for all classes. c. What percentage of the families have an annual income of $50,000 or higher? d. What percentage of the families have an annual income of $40,000 to less than $60,000?
e. Draw a histogram and a polygon for the relative frequency distribution. 5. The following data give the current prices (in dollars) of stocks of 25 companies. 24.75 34.50 48.50 67.50
75.75 55.25 75.50 54.00
47.25 69.50 73.50 51.50
33.25 41.50 63.75 77.50 55.00 39.50 25.75 40.25 65.25 29.25 55.25 48.50 65.75
a. Construct a frequency distribution table. Take the classes as 20 to less than 30, 30 to less than 40, ... , and 70 to less than 80. b. Calculate the relative frequencies and percentages for all classes. c. What percentage of the corporations have their stock prices less than $50? d. Draw a histogram and a polygon for the percentage distribution. 6. The following data give the number of telephones owned by a sample of 30 families. 2 1 3 a. b. c. d. e.
4 1 3
3 2 2
1 2 1
1 4 3
5 3 1
4 3 4
2 1 2
2 5 3
3 2 1
Construct a frequency distribution table using single-valued classes. Calculate the relative frequencies and percentages for all classes. What percentage of the families own two or three telephones? What percentage of the families own three or more telephones? Draw a bar graph for the frequency distribution.
7. The following data give the commuting time (in minutes) from home to school for 30 college students. 22 19 36
16 8 27
11 21 8
12 28 23
23 15 37
51 43 18
42 5 13
6 19 29
31 7 17
10 14 9
Prepare a stem-and-leaf display. Arrange the leaves for each stem in increasing order.
8. Consider the following stem-and-leaf display. 0-2 3-4 6-7 8-9
37••589 1368•02479 113567•2679 23366•778
Write the data set that corresponds to this stem-and-leaf display. 9.A sociologist is doing a study to try to determine the percentage of people in the U.S. who do not have any health insurance coverage. One thousand large communities participated in the study. The grouped data is:
Percent Uninsured 0–4 5–9 10 – 14 15 – 19 20 – 24 25 – 29 30 – 34 35 – 39 40 – 44 45 – 49
f 10 95 225 354 161 59 41 25 15 15
Construct an ogive to describe this data. 10. A research company asked 500 people: “What was the last grade of school you completed?” The grouped data is as follows: Education Level Grade School Some High School High School Grad Some College College Grad Some Postgraduate
Number of Respondents 10 30 185 145 65 65
Construct a pie chart for this data. What percentage of the people did not take any postgraduate courses? 11. If a histogram of major league baseball player salaries is constructed, what shape will the histogram have?