One type of biased sample is a convenience sample. A convenience sample is biased because it only includes people or objects that are easily accessible to the researcher. For example, surveying only students in one class about their favorite subject would be a convenience sample since it's convenient to survey that class. However, it would not represent all students and would be biased since students in that particular class may have different preferences than students in other classes. The sample would not accurately represent the entire population it is trying to make inferences about.

1. Solve.
1. A survey of high school students showed that 63% of students planned to
take college courses after graduation. Predict how many of the 837 students
surveyed plan to take college courses.
2. According to a survey, 73% of adults 21–30 years old own at least one car.
For a city with about 24,600 adults aged 21–30 years, predict how many own
a car.
3. 832 families were asked if they ate dinner together at least 4 nights of the
week. If 62% of the families said yes, predict how many families eat dinner
together at least 4 nights of the week.
4. In a lumberyard, about 13% of its total stored wood is lost to water damage
each year. If the lumberyard stores 250 tons of wood each year, predict how
much is lost to water damage.
Course 2, Lesson 10-2

2. Course 2, Lesson 10-2
ANSWERS
1. 527
2. 17,958
3. 516
4. 32.5 tons

3. HOW do you know
which type of graph to use
when displaying data?
Statistics and Probability
Course 2, Lesson 10-2

4. Course 2, Lesson 10-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Statistics and Probability
• 7.SP.1
Understand that statistics can be used to gain information about a
population by examining a sample of the population;
generalizations about a population from a sample are valid only if
the sample is representative of that population. Understand that
random sampling tends to produce representative samples and
support valid inferences.
• 7.SP.2
Use data from a random sample to draw inferences about a
population with an unknown characteristic of interest. Generate
multiple samples (or simulated samples) of the same size to gauge
the variation in estimates or predictions.

5. Course 2, Lesson 10-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Statistics and Probability
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.

6. • To determine if a sample is
biased or unbiased
• To use sampling to make a
prediction
Course 2, Lesson 10-2
Statistics and Probability

7. Course 2, Lesson 10-2
Statistics and Probability
• unbiased sample
• simple random sample
• systematic random sample
• biased sample
• convenience sample
• voluntary response sample

8. 1
Need Another Example?
Step-by-Step Example
1. A random sample of students at a middle school shows
that 10 students prefer listening to rock, 15 students prefer
listening to hip hop, and 25 students prefer no music while
they exercise. It can be concluded that half the students
prefer no music while they exercise.
This is a simple random sample. So, the sample is unbiased and the
conclusion is valid.
Determine whether the conclusion is valid.
Justify your answer.

9. Answer
Need Another Example?
One classroom of students is surveyed to determine
the theme for the spring dance. Out of 25 students,
15 chose Blast from the Past. The dance committee
concluded that 60% of the students like this theme
best. Is the sample method valid? Justify your
answer.
The conclusion is not valid. This is a
biased convenience sample since only
one classroom is surveyed.

10. 1
Need Another Example?
Step-by-Step Example
2. Every tenth person who walks into a department store is surveyed to
determine his or her music preference. Out of 150 customers, 70
stated that they prefer rock music. The manager concludes that about
half of all customers prefer rock music.
Since the population is every tenth customer of a department store,
the sample is an unbiased, systematic random sample. The
conclusion is valid.
Determine whether the conclusion is valid.
Justify your answer.

11. Answer
Need Another Example?
Every tenth student who walked into the cafeteria
was surveyed to determine his or her favorite
lunch. Out of 40 students, 19 students stated that
they liked the burgers best. The staff concluded
that about 50% of the students like burgers best.
Is the sample method valid? Justify your answer.
The conclusion is valid. This is an unbiased
systematic random sample.

12. 1
Need Another Example?
Step-by-Step Example
3. The customers of a music
store are surveyed to
determine their
favorite leisure
time activity. The
results are shown
in the graph. The store
manager concludes that
most people prefer to listen
to music in their leisure time.
The customers of a music store probably like to listen to music in their
leisure time. The sample is a biased, convenience sample since all of
the people surveyed are in one specific location. The conclusion is
not valid.
Determine whether the conclusion is valid.
Justify your answer.

13. Answer
Need Another Example?
Janet surveyed the athletes on the girls’ field
hockey team to determine which sports
teenagers like best. Of these, 65% said that
they like field hockey best. Janet concluded
that over half of teenagers like field hockey
best. Is the sample method valid? Justify your
answer.
The conclusion is not valid. This is a
biased sample because Janet used a
convenience sample.

14. 1
Need Another Example?
2
3
Step-by-Step Example
4. A store sells 3 types of pants:
jeans, capris, and cargos. The
store workers survey 50
customers at random about their
favorite type of pants. The survey
responses are indicated at the
right. If 450 pairs of pants are
ordered, how many should be
jeans?
First, determine whether the sample method is valid. The sample is a
simple random sample since customers were randomly selected.
Thus, the sample method is valid.
or 50% of the customers prefer jeans.
So, find 50% of 450.
0.5 × 450 = 225, so about 225 pairs of jeans should be ordered.

15. Answer
Need Another Example?
The library is trying to decide what types of books to sell at its book
fair. It surveyed 40 students at random. The results are in the table.
If 220 books are to be sold at the book fair, how many should be
mysteries?
66 books

16. How did what you learned
today help you answer the
HOW do you know
which type of graph to use
when displaying data?
Course 2, Lesson 10-2
GeometryStatistics and Probability

17. How did what you learned
today help you answer the
HOW do you know
which type of graph to use
when displaying data?
Course 2, Lesson 10-2
GeometryStatistics and Probability
Sample answers:
• When determining if a conclusion is valid based upon
the sampling method used
• When using a valid sampling to make a prediction in a
real-world context

18. Name one type of biased
sample and explain the bias.
Course 2, Lesson 10-2
Ratios and Proportional RelationshipsFunctionsStatistics and Probability