Foundations to Algebra
In Class: Representative Samples
Name ________________
Date _________________
Is the survey fair?
If you want to know what a bowl of soup tastes like, do you need to eat all of the soup
in the bowl? Or can you get a good idea of the taste by trying a small sample?
When you conduct a survey, it is not usually possible for you to survey every person in
the population you are interested, such as all female teenage shoppers or all of the
students at your school. Instead, statisiticians collect information about a sample (a
portion) of the population. However, finding a representative sample (a sample that
represents the whole population well) is not easy.
1. As the social director of the Class Council, Ramin would like to survey a few students
about their interests.
When Ramin analyzes the results from the survey, he wants to make claims about
the interests of all of the students in his school. If he were to survey only students
on the Class Council, for example, it might be hard to make claims about what all
students think. Students who are on the Class Council may not have the same
social interests as other students. Consider this idea as you think about the samples
described below.
a. If Ramin wanted to generalize the opinions of all students at his school,
would it make sense to got to the grocery store and survey the people there?
Why or why not?
b. If he wanted to generalize the opinions of all students at his school, would it
make sense to ask all of his friends at school? Why or why not?
c. If he wanted to generalize the opinions of all students at his school, would it
make sense to ask every third person who entered the cafeteria at lunch?
Why or why not?
2. There are a variety of ways to choose samples of the
population you are studying. Every sample has features that
make it more or less representative of the larger population.
For example, if you want to represent all of the students at
your school, but you survey all of the students at school 30
minutes after the last class has ended, you are likely to get a
disproportionate number of students who play school sports,
attend after-school activities, or go to after-school tutoring.
a. If you ask the opinion of the people around you, then you have used a
convenience sample. If you took a convenience sample right now, what
would be some features of the sample? Would you expect a convenience
sample to represent the entire student population at your school? Why or
why not?
b. If you email or create an online questionnaire then you have used a voluntary
response sample. What are some features of the people in a voluntary
response sample? Could it represent the sample of all of the students at
school accurately?
c. If you believe an existing group of people represent all of the students at
your school well enough, this group is a cluster sample. What cluster of
students might you survey at your school to represent the students at your
school? Explain. Are there any reasons that this cluster might not be fully
representative of all the students at your school?
3. From what population is each of these samples taken? Write down the actual
population for each of these sampling techniques.
Method of Sampling
Call every hundredth name in the phone book
Survey people who come to the “Vote Now”
booth at the high school football game.
Ask every tenth student entering a high school
football game
Haphazardly survey students during morning
break
Description of Actual Population
People with phones who also have their numbers
listed
Text response to an online “instant” poll
Hand out surveys in the library before school
Survey all students in Period 1 English classes
4. A study at the University of Iowa in 2008 concluded that children that play violent
video games are more aggressive in real life. Children ages 9 to 12 were studied to
determine how much they played violent video games; peers and teachers were
asked how much these students hit, kicked, and got into fights with other students.
a. Can you legitimately conclude from this study that teenagers who play violent
video games tend to be more aggressive? Why or why not?
b. Can you legitimately conclude from this study that children ages 9 to 12 who
play violent video games are more likely to commit violent crimes? Why or
why not?
c. Can you legitimately conclude from this study that children ages 9 to 12 tend
to hit and kick more in school?
d. Can you legitimately conclude from this study that playing a lot of violent
video games will cause 9 to 12-year-old students to become more violent at
school?
5. Addie was helping children in a kindergarten class learn to read. She was curious
how old the typical child was when they entered kindergarten. It was not practical
to look up the school records of all 100 kindergarteners. On the first day of school,
Addie took a sample: she asked the parent of the first fifteen students to be
dropped off at the school how old (in months) their child was. Her data is listed
below:
67 61 69 72 71 65 67 67 57 68 71 72 61 59 62
Make an inference (a statistical prediction) of the mean age of kindergarten children
at the school.
Foundations to Algebra
Representative Samples HOMEWORK
Name ____________________
Date _____________________
1. Suppose you were conducting a survey to try to determine what portion of voters in
your small town support a particular candidate for mayor. Consider each of the
following methods for sampling the voting population of your town. State whether
each is likely to produce a representative sample and explain your reasoning.
a. Ask every voter on your block.
b. Randomly pick one house from each block in the neighborhood and survey the
homeowner.
c.
Survey each person at the I-Jump Pancake Restaurant after church on Sunday
morning.
d. Ask people who are leaving the twice-yearly town hall meeting.
e. Visit every tenth person on the county’s voter registration list.
2. Fill in the proportions table below and then answer the following questions.
# of cookies
# of calories
a.
0
1
3
120
10
200
What is the unit price?
b. Write an equation that represents the number of calories for any given number
of cookies
3. Solve each proportion.
a.
4
5
= 22
b.
2
3
= 18
c.
5
8
= 12
d.
3
4
= 18
4. Use the graph below to answer the following questions.
a. Is this a proportional relationship? How do you know?
b. What is the constant of proportionality?
c.
How much would it cost for 11 notebooks?
5. 3 batches of cookies need 2 cups of sugar. How many cups of sugar would you
need for 8 batches? Be exact!