Lesson APR-9 examples of biased and unbiased samples.

Lesson APR-9
Teaching Point: Students will determine a representative sample by studying
examples of biased and unbiased samples.
Homework APR-9: Impact, page 289 #10 and Representative Sample
Do Now:
State Test Prep: Which expression below is equivalent to
b. (
d. (
Representative Sample: a sample with an equivalent ratio to that of the
Unbiased Sample: a sample that accurately represents the entire population
Biased Sample: one or more parts of the population that favors one
characteristic over another
Lesson APR-9
Anyone conducting a survey using a sample will want a method that is
practical to perform.
That gives three important questions to ask when examining whether a
particular survey method is a good one.
 Is the sample large enough to give accurate results?
 Is the sample representative of the population?
 Is the survey method practical?
There are two types of Unbiased Samples:
 Simple Random Sample: Each item or person in the population is as
likely to be chosen as any other. For example, if each student’s name is
written on a piece of paper and the place in a bowl to be picked without
 Systematic Random Sample: the items or people are selected according
to a specific time or item interval. For example, if every 20th person is
chosen from an alphabetical list of students attending a school
There are two different ways that a sample can be Biased:
 Convenience Sample: members of a population that are easily accessed.
For example, to represent all the students attending a school, the
principal surveys the students in one math class.
 Voluntary Response Sample: only those who want to participate in the
sampling. For example, students at a school who wish to express their
opinions complete an online survey
Think and Discuss – Groups (Impact page 283)
For a statistics project, Alison’s group wanted to predict which of the
following after-school activities were the favorites of seventh graders in the
four schools in their district:
 playing sports
 playing music
 listening to music
 watching TV
 going to the mall
 playing video games
 reading
 drawing or painting
How would you recommend that Alison’s group collect a sample that would
help them make an accurate prediction? Make a list of suggestions.
Lesson APR-9
Develop and Understand: A – Groups (Impact page 284)
Alison’s group proposed five strategies for conducting its survey.
Strategy 1: Ask all 600 seventh graders in the four schools.
Strategy 2: Distribute questionnaires to the 130 seventh graders at the
district band competition next week.
Strategy 3: Get a list of all the seventh graders in the district. Call 5% at
random from each school.
Strategy 4: Survey every third seventh grader out of the 125 in our school as
they enter their homerooms.
Strategy 5: Survey the 12 seventh graders on one student’s bus.
1. Which strategy or strategies do you think would give the least
representative data? The most representative data?
2. Which strategy would give the smallest sample size? The largest
sample size?
3. Which strategy seems the least practical? The most practical?
4. Which strategy do you think is the best? Explain your reasoning.
Lesson APR-9
Develop and Understand: B – Groups (Impact, page 285)
Alison’s group decided to survey every fourth student to enter each seventh
grade homeroom in the school. The six homerooms have 28 students each.
The survey results are displayed below in a bar graph:
Hours Spent
Favorite After-School Activities
Playing Watching Playing
Going to Listening Reading
the mall to music
1. How large is the sample of the students surveyed?
2. How many students in the sample prefer playing sports after school?
3. Based on the sample, predict how many in a district of 600 seventh
graders would prefer reading?
4. Suppose you could choose one seventh grader from the 600 in Alison’s
school district at random. What is the probability that he or she prefers
playing video games? Explain how you found your answer.
5. If Alison was predicting the favorite leisure activities of all students in
the district, from kindergarten to twelfth grade, would sampling only
seventh graders give an accurate picture of the population? Explain.
Lesson APR-9
Independent Practice
Determine whether each conclusion is valid. Justify your answer.
1. To evaluate the quality of their product, a manufacturer of cell phones
checks every 50th phone off the assembly line. Out of 200 phones
tested, 4 are defective. The manager concludes that about 2% of the cell
phones produced will be defective.
2. To determine whether the students will attend an arts festival at the
school, Oliver surveys his friend in the art club. All of Oliver’s friends
plan to attend. So, Oliver assumes that all the students at his school will
also attend.
3. A random sample of people at a mall shows that 22 prefer to take a
family trip by car, 18 prefer to travel by plane, and 4 prefer to travel by
bus. Is the sample method valid? If so, how many people out of 500
would you expect to say they prefer to travel by plane?
Preferred Ways to Travel