Academic Worksheet 11.1 – Stem-and-Leaf Plots
Make an ordered stem-and-leaf plot of the data.
1. 10, 23, 55, 76, 88, 21, 30, 43, 56, 67, 78, 89, 43, 41, 54, 60
2. 16.9, 17.8, 16.3, 16.4, 17.8, 18.1, 15.4, 16.8, 17.1, 18.3, 15.5, 16.2, 17.9
3. 282, 274, 250, 291, 286, 249, 289, 288, 251, 261, 272, 268, 247, 263, 248, 267, 295, 287
4. The ages of 30 people who participate in a contest are as follows: 23, 25, 37, 44, 48, 39, 33, 27,
28, 41, 19, 18, 22, 29, 35, 46, 47, 31, 30, 20, 34, 37, 41, 45, 25, 28, 34, 45, 40, 18
a. Make an ordered stem-and-leaf plot of the data.
b. Find the median and range of the data.
5. The stem-and-leaf plot shows the times (in minutes) for 30 men who completed the 2002
Boston Marathon using a wheelchair.
a. What was the fastest time?
b. Find the median of the times.
c. What percent of the participants
finished the race in less than 2 hours?
d. The fastest female wheelchair time in
the marathon was 1 hour 46 minutes.
How does this time compare with the
times of the 30 male participants?
6.
Answer the following questions using the stem-and-leaf plot below.
a. What is the lowest value?
b. What is the greatest value?
c. What is the median?
d. What is the range?
Academic Worksheet 11.1 – Frequency Tables and Histograms
Use the data to make a frequency table and a histogram.
1. Use intervals of 4, starting at 4: 20, 4, 6, 9, 14, 15, 20, 23, 21, 7, 4, 12, 10, 5
2. Use intervals of 10, starting at 241: 281, 241, 267, 290, 283, 281, 282, 284, 262, 271, 274, 285,
261, 284, 283, 280, 275
3. Make a histogram of the following ages (in years) of customers in a store. 27, 11, 39, 21, 45, 23,
42, 28, 30, 16, 31, 42, 35, 38, 17, 40, 35, 31. Use intervals of 10 starting at 10.
4. The histogram shows the times (in minutes) for 30 women who completed a 5K road race.
a. What interval has the greatest frequency?
b. About what percent of the participants
finished the race in less than 30 minutes?
c. The average men’s time in the race was 28
minutes. How does this compare to the
women’s times? Explain.
5. The histogram shows the average number of vacation days that working citizens in 30 major
cities in Europe and North America have each year.
a. What interval has the greatest frequency?
b. In what percent of the cities surveyed do working
citizens have fewer than 20 vacation days per
year?
c. Citizens of Shanghai, China, average 16 vacation
days per year. How does Shanghai compare with
the data given for North America and Europe?
Explain.
6. The histogram shows the amounts (in dollars) spent on purchases in a store. Make three
conclusions about the data in the following histogram.
Academic Worksheet 11.2
Make a box-and-whisker plot of the data.
1. Number of hours of television watched per day: 1, 5, 0, 2, 7, 3, 4, 6
2. Jean prices (in dollars): 23, 13, 12, 19, 27, 30, 18, 40, 14, 25, 20
The box-and-whisker plot shows the average monthly temperatures for Erie, Pennsylvania. Estimate the
value.
3. lower extreme
4. upper extreme
5. range
6. lower quartile
7. upper quartile
8. interquartile range
In Exercises 9 – 11, use the following information. The data below are the average monthly
temperatures (in degrees Fahrenheit) for Buffalo and San Diego.
Buffalo: 24, 26, 34, 45, 57, 66, 71, 69, 62, 51, 40, 30
San Diego: 58, 59, 60, 63, 65, 67, 71, 73, 72, 68, 62, 58
9. Make a box-and-whisker plot for each data set. Draw both box-and-whisker plots using the same
number line.
10. Compare the range and the interquartile range for the two data sets.
11. About what percent of the average monthly temperatures in Buffalo are less than 64°F? About what
percent of the average monthly temperatures in San Diego are less than 64°F?
Academic Worksheet 11.3
Tell whether the data are numerical or categorical. Then tell which display(s) you would use to display
the data. Explain your reasoning.
1. A survey was conducted where the
2. A zookeeper recorded the weights of the
responses were agree, disagree, and
baby animals in the zoo
unsure
3. A study determined the average winning
score of high school soccer teams
4. A meteorologist recorded the amount of
rainfall in 3 states over one year
5. A study was done that asked people what
month of the year they like to take
vacations
6. A researcher recorded the number of
visitors to nation museums in the United
States during the last 5 years
7. A teacher recorded the heights of students
in a class
8. A coach recorded the number of goals
scored by each member of a hockey team
Tell which data display(s) allow you to identify the specified information.
9. The range of the data set
10. The least data value
11. The median of the data set
12. The greatest value of the data set
13. The mode of the data set
14. The frequency of an interval
15. A teacher records the scores on a project and wants to group the data in intervals of 5 points.
Should the teacher use a stem-and-leaf plot or a histogram? Explain.
16. Thirty people were asked to state the number of
hours per week that they commute to and from
work in a car. The frequency table shows the
results.
a. Is the frequency table misleading?
Explain.
b. What conclusions can you make from the
frequency table?
17. The line graph shows the number of visitors to national parks in the United States over seven
years. Is the graph misleading?
Explain.
Academic Worksheet 11.4
A newspaper is conducting a survey to predict who will win the next mayoral election. Tell whether the
sampling method is random, systematic, stratified, convenience, or self-selected.
1. Set up a phone number where people call
2. Call every 100th person in the phone book
in their opinion
3. Interview the first 50 people who leave a
4. Interview 10 people from each
grocery store
neighborhood
A school newspaper is conducting a survey to predict who will win the next school election. Tell
whether the sampling method is random, systematic , stratified, convenience, or self-selected.
5. Set up a booth where students can come
6. Get the ID numbers of every student in the
give their opinions
school and have a computer randomly
choose which students will be surveyed
7. Interview every third student as students
8. Interview 20 students from each grade
leave the school
In Exercises 9 and 10, describe the population and tell what type of sampling method is used. Then tell
whether the sample is likely to represent the population. Explain your answer.
9. A book store clerk wants to determine the most popular magazine in the store. The clerk posts
a sign asking interested customers to complete a survey found at the checkout.
10. A writer for a magazine wants to determine the most popular flavor of ice cream among
residents in a town. The writer asks each customer at several local ice cream shops what their
favorite flavor of ice cream is.
11. A speaker at a seminar wants to know how well a
speech was received by members of the audience. The
speaker leaves the form shown on a table for members
of the audience to complete after the speech.
a. Describe the population and the sampling
method.
b. Is the questionnaire likely to represent the
population? Explain why or why not.
In Exercises 12 – 14, tell whether the question is potentially biased. Explain your answer. If the question
is biased, rewrite it so that it is not.
12. Do you support building an expensive new stadium while the old one is perfectly usable?
13. How many times a week do you exercise?
14. Don’t you think our town should have a fun new park?
15. Researchers conducted a study to determine the average age of the people living in a city. They did
so by recording the age of 200 people in the city. Tell whether the following statements, if true,
would lower your confidence in the results of the study. Explain your answers.
a. The researchers chose the people in their sample randomly.
b. The researchers selected people only from the eastern portion of the city.
c. Some of the people in the study were much older than others.
Academic Worksheet 11.5
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A survey of 300 randomly selected new parents finds that 99 new parents prefer brand A baby
food. Predict how many new parents in a town of 2500 new parents prefer brand A baby food.
You interview a random sample of 100 residents in a town. Forty-two people say that raspberry
is their favorite muffin flavor. There are 3000 people in the town. Predict how many people in
the town would say that raspberry is their favorite muffin flavor.
Two surveys based on random samples of students in a school were conducted before a school
student council election. For each election, predict a winner or tell whether the election is too
close to call. The margin of error is  4% for each survey.
a. Presidential Election: Leading Candidate 52%, Trailing Candidate 48%
b. Vice President Election: Leading Candidate 55%, Trailing Candidate 45%
A politician needs 750 signatures from people in town to run for office. You interview a random
sample of 100 people in town. You find that 38 people say they would provide their signature.
The town has 3200 people. Do you think enough people will provide their signatures? Justify
your reasoning.
A town has 2500 residents. A survey finds that 92 residents out of a random sample of 575
residents have a red car. The margin of error for the survey is  4% . Find the interval in which
the total number of residents with a red car is most likely to lie.
Suppose there are 20 students in your math class. Four of the students have the flu. Can you
use this information to predict how many people in your own town have the flu? Explain why or
why not.
A survey with a margin of error is +-2% find that history is the favorite subject of 39% of a
random sample of students. In which interval is the population percent most likely to lie?
Review the newspaper article below which summarizes the results of a survey. How much trust
do you have in the survey? Do you think the conclusions in the article are valid? Explain.