POPULATION AND SAMPLE
Sizing up survey results
Statistics can be used to make generalizations about a population. A POPULATION is the
group of interest. It is usually not possible to gather data from each member of a population, so
the generalizations are often based upon a sample. A SAMPLE is a smaller group taken from the
population.
Samples allow researchers to save time and money when gathering information. Samples are
only useful if they are representative of the population. A REPRESENTATIVE SAMPLE is a
portion of the population that is similar to the entire population. A BIASED SAMPLE is one in
which some members of the population have a greater chance of being selected for the sample
than other members. Because of bias, the sample does not fairly represent the population.
One way to gather information is by surveying the members of the sample. A SURVEY is a
question of set of questions used to gather DATA, or pieces of information. A survey can also be
biased
EXAMPLE 1
Reggie thinks that more students in his school are right-handed than left handed. He surveys the
students in his class and finds that 23 of the 27 students are right – handed. Do the results of
Reggie’s survey support his inference that more students in his school are right-handed than lefthanded?
Does Reggie’s results support his claim that more students in his school are right – handed
than left handed?
RANDOM SAMPLES are usually preferred when gathering information about a population. In a
random sample, each individual in the population has an equal chance of being part of the
sample.
EXAMPLE 2
Collin asked every eighth student entering the school which of four subjects was his or her
favorite. Can the results of Collin’s survey be used to draw inferences about students’ favorite
subjects at the school?
Decide if the sample is a representative and the survey is unbiased.
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EXAMPLE 3
The table below shows the results of Collin’s survey from example 2
Subject
Number of Students
15
20
10
5
Math
Science
Language Arts
Social Studies
There are 400 students at Collin’s school. How many students would you predict prefer
language, if he continued to survey?
STRATEGY: Write and solve a proportion
STEP 1: Add to find the total number of students Collin surveyed.
_____ + _____ + ______ + ______ = _______
STEP 2: Write a proportion
Have each ratio show the number of students who prefer language arts to the total
number of students. Let x represent all of the students at the school who prefer language arts.
=
STEP 3: Cross multiply and solve for x.
_______ x _______ = ________ x _________
SOLUTION: Out of 400 students, _______ students would probably say they prefer language
arts.
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EXAMPLE 4
Which two of the following samples are NOT good samples? Explain why.
A. Every third shopper at a clothing store is asked whether he or she owns a pet.
B. Every third shopper at a pet store is asked whether he or she owns a pet
C. At the beach in the summer, 150 people are asked to name their favorite vacation spot.
D. A survey is mailed to 50 homes in a neighborhood, asking residents to name their favorite
vacation spot.
Now that we have worked a few examples, let us try some independent practice.
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Lesson Practice
Choose the correct answer.
1. Martha is planning to survey people at a
water park to determine the most popular
water slide at the park. Which would be the
best sample for her survey to draw a valid
inference?
A. Children at the park between the ages of
3 and 5
B. Children at the park between the ages of
6 and 10
C. Adults at the park between the ages of 20
and 30.
Use the information below for questions 3
and 4.
Mr. Callahan just opened a flower shop. He
took a random survey of shoppers to find out
their favorite flowers and recorded the
results in the table below.
Favorite Flower
Type
Daffodil
Lily
Rose
Daisy
Shoppers
14
10
24
12
D. Adults and children of all ages at the park
2. A newspaper is conducting a survey to
determine which American professional
baseball team is most popular. How would it
most likely get a random sample that is
representative of the population?
3. What is the size of the sample?
A. 4
B. 50
C. 60
A. By asking people at a Florida Marlins
game
B. By calling people from around the
country
C. By asking every fifth person entering the
stadium at a Red Sox Game
D. 64
4. If Mr. Callahan expects to sell 150
bunches of flowers next week, which is the
best prediction of how many bunches of
daffodils he should have in his shop?
A. 28
D. By asking people at a Cincinnati Reds
game
B. 35
C. 42
D. 60
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5. Which of these is NOT a random sample that
would be valid to determine the favorite food of
students in your school?
A. five students at a local pizza parlor
6. Miko took a survey of the students in her grade to see
how many are likely to join a book club in she starts one.
She surveyed 48 students, and ten said they would join.
If there are 240 students in her grade, how many students
might Miko expect to join club?
B. every sixth student on the school roster
A. 28
C. every tenth student entering school in the
morning
B. 38
C. 48
D. three students from each table in the lunchroom
D. 50
7. A survey asked students at a middle school which of four after-school sports they would most like
to have at their school. The students who participated in the survey were randomly selected during
their lunch period. The results are shown in the table below.
After – School Sports
Sport
Number of Students
Track
22
Cross – Country
15
Lacrosse
48
Tennis
15
A. Identify the sample and the population. Is the sample representative of the population?
Explain your thinking.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
B. If you assume that the sample is representative of the population, how many students would
you predict to choose lacrosse in a school of 750 students? Is the prediction a good prediction?
Explain.
____________________________________________________________________________
____________________________________________________________________________
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8. Delores is curious about how many times
a week students in seventh grade exercise
each week. Which sample below is biased?
A. A sample consisting of students on sports
teams
B. A sample of every fifth student that
enters the school
C. A sample consisting of one student
randomly chosen from each homeroom
D. A sample of consisting of every tenth
student from an alphabetical roster of the
school.
9. Brandon wants to conduct a survey that
asks which flavor of chips is preferred, Hot
Cheetos or Sweet Chilli Doritos, among
seventh grade students. Which method will
offer Brandon the BEST results?
Use the information below to answer
questions 10 – 11.
Nate surveyed Random people walking into
Wal-Mart. He wanted to find out which new
Granola Bar they would like the store to sell.
Granola Flavor
Chocolate Cherry
Peanut Delight
Berry Blast
Honey Chocolate
Number of people
20
15
30
10
10. What is the size of the sample?
A. 10
B. 30
C. 50
D. 75
A Interview every student eating hot
Cheetos
11. If Brandon surveys 825 more people,
how many people can he predict to pick
Honey Chocolate?
B. Interview every student that buys Sweet
Chili Doritos
A. 107
C. Interview every seventh grade who eats
lunch in the school cafeteria
D. Interview every student that does not buy
chips
B. 150
C. 210
D. 110
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12. Which situation would provide a random
sample size?
Use the information below to answer
questions 14 – 15
A. Determining the most popular baseball
team by surveying every tenth person
coming out of a New York Yankee’s Game
Kailyn surveyed every girl at Central Middle
School on their favorite tv show. The results
are shown below
B. Determining the most common degree
program in the country by surveying every
tenth student at one college campus.
TV SHOW
C. Determining the favorite summer activity
of students in your school by surveying
every tenth student in entering every
classroom.
D. Determining America’s favorite hip-pop
artist by surveying every fifth person
attending a Rihanna concert
13. Daijzon is planning to survey people at
Six Flags to determine the most popular
roller coaster at the park. Which would be
the best sample for her survey to draw a
valid inference?
A. Every sixth person in line at Batman
Roller Coaster
106 & park
Snooki & Jwowwi
Spongebob
Boondocks
Number of
Students
20
15
25
10
14. What is the sample size of the survey?
A. 20
B. 70
C. 60
D. 50
15. Kailyn wanted to survey 540 more
students at Central Middle School. How
many students could she predict to pick 106
& park?
B. Every tenth person in line at the wacky
twist
A. 154
C. Every sixth person leaving the park
C. 360
D. Every eighth person getting out of their
car.
D. 400
B. 250
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