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Chapter 2: Review Questions Mr. Lynch
Why do we need to group data in the form of a frequency table? Explain briefly.
How are the relative frequencies and percentages of categories obtained from the frequencies of categories?
The following data give the results of a sample survey. The letters A, B, and C represent the three categories.
A B B A C B C C C A
C B C A C C B C C A
A B C C B C B A C A
Prepare a frequency distribution table.
Calculate the relative frequencies and percentages for all categories.
What percentage of the elements in this sample belong to category B?
What percentage of the elements in this sample belong to category A or C?
Draw a bar graph for the frequency distribution.
The following data give the results of a sample survey. The letters Y, N, and D represent the three categories.
D N N Y Y Y N Y D Y
Y Y Y Y N Y Y N N Y
N Y Y N D N Y Y Y Y
Y Y N N Y Y N N D Y
Prepare a frequency distribution table.
Calculate the relative frequencies and percentages for all categories.
What percentage of the elements in this sample belong to category Y?
What percentage of the elements in this sample belong to category N or D?
Draw a pie chart for the frequency distribution.
Thirty adults were asked which of the following conveniences they would find the most difficult to do without: television (T), refrigerator (R), air conditioning (A), or microwave (M). Their responses are listed below:
R A R P P T R M P A
A R R T P P T R A A
R P A T R P R A P R
a) Prepare a frequency distribution table.
b) Calculate the relative frequencies and percentages for all categories.
c) What percentage of these adults named refrigerator or air conditioning as the convenience that they would find the most difficult to do without?
d) Draw a bar graph for the relative frequency distribution.
Briefly explain the three decisions that have to be made to group a data set in the form of a frequency distribution table.
How are the relative frequencies and percentages of classes obtained from the frequencies of classes? Illustrate with the help of an example.
Three methods were discussed to group quantitative data into classes. Explain these three methods and give one example of each.
A sample of 80 adults was taken and these adults were asked about the number of credit cards they possess. The following table gives the frequency distribution of their responses:
Number of Credit CardsNumber of Adults0 to 3184 to 7268 to 112212 to 151116 to 193
Find the class boundaries and the class midpoints.
Do all classes have the same width? If so, what is the width?
Prepare the relative frequency and percentage distribution columns.
What percentage of these adults possess 8 or more credit cards?
The following table gives the frequency distribution of ages for all 50 employees of a company.
AgeNumber of Employees18 to 301231 to 431944 to 561457 to 695
Find the class boundaries and the class midpoints.
Do all classes have the same width? If so, what is the width?
Prepare the relative frequency and percentage distribution columns.
What percentage of employees of this company are age 43 or younger?
A data set on money spent on lottery tickets during the past year by 200 households has a lowest value of $1 and a highest value of $1,167. Suppose we want to group these data into six classes of equal width.
Assuming we take the lower limit of the first class as $1 and the width of each class equal to $200, write the class limits for all six classes.
What are the class boundaries and class midpoints?
A data set on monthly expenditures (rounded to the nearest dollar) incurred on fast food by a sample of 500 households has a minimum value of $3 and a maximum value of $147. Suppose we want to group these data into six classes of equal width.
Assuming we take the lower limit of the first class as $1 and the upper limit of the sixth class as $150, write the class limits for all 6 classes.
Determine the class boundaries and class widths.
Find the class midpoint.
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 51 48 46 43 52 50 54 47 44 47 50 49 52
a) Make the frequency distribution table for these data.
b) Calculate the relative frequencies for all classes.
c) Construct a histogram for the relative frequency distribution.
d) Construct a polygon for the relative frequency distribution.
Briefly explain the concept of cumulative frequency distribution. How are the cumulative relative frequencies and the cumulative percentages calculated?
Explain for what kind of frequency distribution an ogive is drawn. Can you think of any use for an ogive? Explain.
The following table gives the frequency distribution of the number of credit card possessed by 80 adults.
Number of Credit CardsNumber of Adults0 to 3184 to 7268 to 112212 to 151116 to 193
Prepare a cumulative frequency distribution.
Find the percentage of these adults who possess 7 or fewer credit cards.
Draw an ogive for the cumulative percentage distribution.
Using the ogive, find the percentage of adults who possess 10 or fewer credit cards.
Briefly explain how to prepare a stem-and-leaf display for a data set. You may use an example to illustrate.
What advantage does preparing a stem-and-leaf display have over grouping a data set using a frequency distribution? Give one example.
The following data give the time (in minutes) that each of 20 students waited in line at their bookstore to pay for their textbooks in the beginning of the Spring 2006 semester:
15 8 23 21 5 17 31 22 34 6 5 10 14 17 16 25 30 3 31 19
a) Construct a stem-and-leaf display for these data. Arrange the leaves for each stem in increasing order.
The following are the total yards gained rushing during the 2005 season by 14 running backs of 14 college football teams:
745 921 1133 1024 848 775 800 1009 1275 857 933 1145 967 995
a) Construct a stem-and-leaf display for these data. Arrange the leaves for each stem in increasing order.
Briefly explain how to prepare a dotplot for a data set. You may use an example to illustrate.
What is a stacked dotplot and how is it used?
Create a dotplot for the following data set:
1 2 0 5 1 1 3 2 0 5 2 1 2 1 2 0 1 3 1 2
The following table gives the number of stolen bases during the 2005 season by some of the members of the Boston Red Sox:
PlayerStolen BasesJ. Damon19D. Ortiz0M. Ramirez2J. Varitek10N. Garciaparra2K. Youkilis0
Create a dotplot for the following data set:
Mention any clusters or outliers you observe.
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