31
Objective
Predict the actions of a larger group by using a sample
Vocabulary
Sample
A randomly selected group chosen for the purpose of collecting data
Vocabulary
Population
The entire group of items or individuals from which the samples under consideration are
taken
Vocabulary
Unbiased sample
A sample that is selected so that it is representative of the entire population
Vocabulary
Simple random sample
A sample where each item or person in the population is as likely to be chosen as any
other
Vocabulary
Stratified random sample
A sampling method in which the population is divided into similar, non-overlapping groups
Vocabulary
Systematic random sample
A sampling method in which the items or people are selected according to a specific
time or item interval
Vocabulary
Biased sample
A sample drawn in such a way that one or more parts of the population are favored over others
Vocabulary
Convenience sample
A sample which includes members of the population that are easily accessed
Vocabulary
Voluntary response sample
A sample which involves only those who want to participate in the sampling
Example 1 Describe Samples
Example 2 Describe Samples
Example 3 Using Sampling to Predict
Example 4 Using Sampling to Predict
To determine which school lunches students like most, every twentieth student to walk into the cafeteria is surveyed. Describe the sample.
Answer: Random, unbiased
Every 20th student is surveyed
1/4
Random sample
Population is those entering cafeteria
Unbiased
To determine which CDs customers like most, every tenth customer to walk into the music store is surveyed. Describe the sample.
Answer: Unbiased, random
1/4
To determine what sports teenagers like, the student athletes on the girls’ field hockey team are surveyed. Describe the sample.
Answer: Biased, Convenience
Girl’s on field hockey team are more likely to choose hockey as favorite sport
2/4
Biased
Only the hockey team is survey
Convenience
To determine what restaurant teenagers like, the teenagers eating at Pete’s Diner are surveyed. Describe the sample.
Answer: Biased, Convenience
2/4
BOOKS The student council is trying to decide what types of books to sell at its annual book fair to help raise money for the eighth-grade trip. It surveys 40 students at random. The books they prefer are in the table. What percent of the students prefer mysteries?
8short stories
11sports
9adventure novel
12mystery
Number of Students
Book Type
Write proportion to find percent
3/4
BOOKS The student council is trying to decide what types of books to sell at its annual book fair to help raise money for the eighth-grade trip. It surveys 40 students at random. The books they prefer are in the table. What percent of the students prefer mysteries?
Remember: Percent has a denominator of 100
x z 100
3/4
Define the variable
The second ratio is based on preference of mystery books to total books
BOOKS The student council is trying to decide what types of books to sell at its annual book fair to help raise money for the eighth-grade trip. It surveys 40 students at random. The books they prefer are in the table. What percent of the students prefer mysteries?
The denominator is the total surveyed40
x z 100
3/4
The numerator is how many prefer mysteries
=
BOOKS The student council is trying to decide what types of books to sell at its annual book fair to help raise money for the eighth-grade trip. It surveys 40 students at random. The books they prefer are in the table. What percent of the students prefer mysteries?
12 preferred mysteries
40 x z 100
3/4
=
8short stories
11sports
9adventure novel
12mystery
Number of Students
Book Type12
BOOKS The student council is trying to decide what types of books to sell at its annual book fair to help raise money for the eighth-grade trip. It surveys 40 students at random. The books they prefer are in the table. What percent of the students prefer mysteries?
Cross multiply40
x z 100
3/4
= 12
40x = 12(100)Multiply
40x = 1200Ask “What is being done by the variable?”
The variable is being multiplied by 40
Do the inverse on both sides of the equal sign
BOOKS The student council is trying to decide what types of books to sell at its annual book fair to help raise money for the eighth-grade trip. It surveys 40 students at random. The books they prefer are in the table. What percent of the students prefer mysteries?
Using a fraction bar, divide both sides by 4040
x z 100
3/4
= 12
40x = 12(100)40x = 120040 40
Combine “like” terms
1 x = 30
Use the Identity Property to multiply 1 x
x = 30
Add dimensional analysis
%Answer:
PENS The student shop sells pens. It surveys 50 students at random. The pens they prefer are in the table. What percent of the students prefer gel pens?
10roller balls
10glitter pens
8ball point
22gel pens
NumberType
Answer: x = 44%
3/4
BOOKS The student council is trying to decide what types of books to sell at its annual book fair to help raise money for the eighth-grade trip. It surveys 40 students at random. The books they prefer are in the table. If 220 books are to be sold at the book fair, how many should be mysteries?
8short stories
11sports
9adventure novel
12mystery
Number of Students
Book Type
Write proportion
4/4
BOOKS The student council is trying to decide what types of books to sell at its annual book fair to help raise money for the eighth-grade trip. It surveys 40 students at random. The books they prefer are in the table. If 220 books are to be sold at the book fair, how many should be mysteries?
8short stories
11sports
9adventure novel
12mystery
Number of Students
Book Type
First ratio is taken from the chart about the survey
4/4
12
BOOKS The student council is trying to decide what types of books to sell at its annual book fair to help raise money for the eighth-grade trip. It surveys 40 students at random. The books they prefer are in the table. If 220 books are to be sold at the book fair, how many should be mysteries?
8short stories
11sports
9adventure novel
12mystery
Number of Students
Book Type
Total surveyed is denominator
4/4
1240
BOOKS The student council is trying to decide what types of books to sell at its annual book fair to help raise money for the eighth-grade trip. It surveys 40 students at random. The books they prefer are in the table. If 220 books are to be sold at the book fair, how many should be mysteries?
The next ratio will be based on how many actually were sold
4/4
1240
The total books sold will be the denominator
220=
Define the variable
x
BOOKS The student council is trying to decide what types of books to sell at its annual book fair to help raise money for the eighth-grade trip. It surveys 40 students at random. The books they prefer are in the table. If 220 books are to be sold at the book fair, how many should be mysteries?
4/4
1240 220
= x Cross multiply
40x = 12(220)
Multiply
40x = 2,640
Ask “What is being done by the variable?”
The variable is being multiplied by 40
Do the inverse on both sides of the equal sign
BOOKS The student council is trying to decide what types of books to sell at its annual book fair to help raise money for the eighth-grade trip. It surveys 40 students at random. The books they prefer are in the table. If 220 books are to be sold at the book fair, how many should be mysteries?
4/4
1240 220
= x
40x = 12(220)40x = 2,640
Using a fraction bar, divide both sides by 40
40 40
Combine “like” terms
1 x = 66
Use the Identity Property to multiply 1 x
x = 66
Add dimensional analysis
mystery booksAnswer:
PENS The student shop sells pens. It surveys 50 students at random. The pens they prefer are in the table. If 300 pens are to be sold at the student shop, how many should be gel pens?
10roller balls
10glitter pens
8ball point
22gel pens
NumberType
Answer: x = 132 gel pens
*
4/4
Assignment
Lesson 8:7Statistics:
Using Sampling to Predict3 - 15 All
