CHAPTER 3
D
Sampling Methods
c GOAL
Determine the differences between using simple random samples and systematic
samples in gathering survey data.
Learn about the Math
When it is necessary to gather data to answer a question
concerning a population, a survey is conducted. A survey is
given to just a portion of the entire population to be studied,
or a sample, to gather data that can then be generalized for
the rest of the population.
There are different types of samples. One type is called a
simple random sample. This is when a survey sample is
chosen in such a way that the entire population has an equal
chance of being selected for the sample.
Another type of sample is a systematic sample. This type
of survey sample is not completely random. It is biased in
some way.
For example, if a survey is conducted using the Internet, then
this survey is biased toward people who use the Internet.
Someone that does not own a computer or does not know
how to use the Internet would not have an equal opportunity
to take part in this survey. The survey then is not representative
of the entire population, only the portion that uses the Internet. A
representative sample is representative of the entire population
with regard to all of its characteristics, meaning that it matches
the proportions of the entire population with regard to factors
such as gender, age groups, race/ethnicity, and geographic
location. The size of the sample must be large enough for all of
the different characteristics to be accurately represented.
sample
a part of a population
that is used to make
predictions about the
whole population
simple random
sample
a survey sample
chosen in such a way
that every member of
the population has an
equal chance of being
included
systematic
sample
a survey sample
chosen in such a way
that it is biased toward
certain members of
the population; all
members of the
population do not
have an equal chance
of being included
Akeem wanted to determine if the students in his school
would be interested in an after-school tutoring program. He
passed out questionnaires to all of the students in his classes,
asking them to complete the survey questions about their
interest in such a program. About half of the students who
received a questionnaire completed and returned it to Akeem.
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3D Sampling Methods
1
Akeem’s survey sample a simple random sample
? Was
or a systematic sample?
Example 1: Determining if a survey sample is
a random sample or a systematic sample
Was Akeem’s survey sample a simple random sample or a systematic sample?
Isabella’s Solution
I can determine the type of survey sample used by examining the definition
of a simple random sample. In order for a sample to be a simple random
sample it has to be chosen in such a way that the entire population has an
equal chance of being selected for the survey.
Akeem only passed out the survey to students in his classes. This means that
any student not having a class with Akeem did not have an opportunity to be
selected for this survey. This survey would then be biased toward Akeem’s
classmates.
Since the after-school tutoring program would be for the entire school, a simple
random sample would have to include participants representative of the entire
school, from all different grade levels and classes. Therefore, I have determined
that Akeem’s sample was a systematic sample, not a simple random sample.
Reflecting
1. Why might a systematic sample not be a good
representation of an entire population?
2. Give an example of a method of conducting a survey that
would result in a simple random sample.
3. Give an example of a sampling method that would result
in a systematic sample.
2
Nelson Mathematics Secondary Year Two, Cycle One
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Work with the Math
Example 2: Determining if a sample is representative
of an entire population
Sarah was conducting a survey to find out how much time, on average,
students in Cycle One Year Two spend on homework each night. She asked
five of her friends, three girls and two boys, to keep track for one week of how
much time they spent on homework each night. The average time was found to
be 3 h. Was Sarah’s sample a good representation of her entire population?
Rodrigo’s Solution
To determine whether or not Sarah’s sample was a good representation of
the population being studied, I needed to decide if her sample was random
and if it was large enough to be representative of the entire population.
First, I looked back at the definition of a simple random sample. A simple
random sample must give every member of the entire population an equal
chance of being selected as part of the sample. Since Sarah polled only her
friends, someone whom Sarah did not know would not have an equal
opportunity to be selected. Therefore, I can determine that this sample
was not a simple random sample.
Next, I must consider the size of the sample. Sarah selected five people to
survey. I can determine that five people would not be a large enough sample to
gather data representative of all Cycle One Year Two students because five
people cannot accurately reflect all of the possible characteristics of the entire
population of Cycle One Year Two students. Therefore, this sample is not a good
representation of the entire population being studied.
I can conclude that Sarah’s sample is neither a simple random sample, nor large
enough to be representative of the entire population.
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3D Sampling Methods
3
A
Checking
4. For each of the following situations,
state the population and whether the
sample is random.
a) A newspaper wants to determine
how people in a community feel
about a landfill in their area. A
reporter stopped four people in the
town and asked their opinion.
b) An automobile manufacturer wants
to find out if a new hybrid vehicle
would sell well nationally. At an auto
show they had a questionnaire for
people to fill out, asking if they
would consider buying the vehicle.
By the end of the show, 1210
surveys were completed.
B
Practising
5. A manufacturing company has
developed a new form of tooth
whitening strip that they believe works
more quickly than competitors’ similar
products. They asked a group of
20 people, chosen at random from
shoppers in a local pharmacy, to try
the new strips for 14 days and then
complete a questionnaire stating their
opinions about the new product. Is the
sample a good representation of the
entire population being studied?
6. Maggie wanted to determine how
other students in her school feel about
having to wear uniforms to school. She
created a survey and distributed it to
everyone in her lunch period. Of the
400 surveys distributed, 205 were
completed and returned. What is
the population of this study? What is
the size of Maggie’s sample? Was the
sample random or systematic?
4
Nelson Mathematics Secondary Year Two, Cycle One
7. Qi wanted to determine the type of
music that is most preferred by
students in his class. He asked 10
of his friends to write down their
favourite type of music. Are the results
of this survey representative of the
preferences of Qi’s entire class?
8. Emily is a reporter for the school
newspaper. She wanted to determine
which candidates were most likely to
win the upcoming school election.
Emily held a mock election, where
students could cast their votes for who
they think the winning candidates
should be. Of the 850 students in
Emily’s school, 320 of them cast a
ballot in this mock election. Students
who were absent were all given an
opportunity to cast an absentee ballot.
What is the population for this study?
Was the sampling method random or
systematic?
9. A cell phone manufacturer selects
every 100th cell phone produced to be
tested for defects. Is this a random
sample or a systematic sample?
C
Extending
10. The Student Council would like to
determine the best way to raise money
for their school carnival. Members of
the Council have listed several types of
fundraisers that could be held. They
would like to perform a survey of
students in the school that would give
them an idea of which fundraiser
would help them raise the most
money. Explain a sampling method
that Student Council members could
use to help them gather the
information needed.
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Copyright © 2009 by Nelson Education Ltd.