# Finding Sales Tax by jennyyingdi

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```									Sampling Methods

Lesson 3-6
Pg. # 103-105
CA Content Standards
Statistics, Data Analysis, and Probability 2.2***:
I can identify different ways of selecting a sample (i.e.
convenience sampling, responses to a survey,
random sampling) and which method makes a
sample more representative for a population.

Statistics, Data Analysis, and Probability 2.4***:
I can identify data that represent sampling errors and
explain why the sample might be biased.
Vocabulary: BIASED
 Survey results in which samples are
chosen or used unfairly.
Vocabulary:
REPRESENTATIVE
 Containing typical examples of all types
in a group.
Vocabulary:
CONVENIENCE SAMPLING
 Sample is formed by choosing individuals
or objects that are convenient, or easy, to
include in the study.

 Usually results in a biased sample.
Vocabulary:
RANDOM SAMPLING
 Sampling in which each individual or item
has an equal chance of being chosen.

 Usually results in a representative, or fair,
sample.
Vocabulary:
SYSTEMATIC SAMPLING
 Sampling that involves a system, method,
or plan.

 Usually results in a representative, or fair,
sample.
Vocabulary:
RESPONSES TO A SURVEY
 Answers to a questionnaire or other
device designed to get information from a
population.

 Usually results in a biased sample
because only people who really care or
have the time will respond to the survey.
Objective

Understand how the method of
sampling determines how
representative the sample is of the
population.
Math Link: You can use what you
know about sampling to find how
sampling methods can affect the
statistical results.
Example 1.

Look at the table on page 103. It shows the
number of school districts in each state.
The five most populated states are
California (CA), Texas (TX), Michigan (MI),
Illinois (IL), and New York (NY). Find the
median number of school districts per state
using these five states as a sample.
MI    NY       IL    CA      TX
674    705     929    994    1042

The median is the middle number in the
sample. According to this sample, there are
approximately 929 school districts in each
state.
A biased sample does not reflect the
population fairly. This sample is biased
because states with large populations are
likely to have more than an average number
of school districts.
Example 2.

The name of each state was written on a
piece of paper and placed in a bag. Then
five pieces of paper were selected without
looking.

The states selected were Maine (ME),
(KS), and Rhode Island (RI).
RI    CO      ME     KS      WI
36    176     284    304     426

The median is the middle number in the
sample. According to this sample, there are
approximately 284 school districts in each
state.
This example uses random sampling. In
random sampling, each school district has
an equal chance of being chosen. Since a
random sample is usually a good match for
the population, it is a representative
sample.
Example 3.

 The principal of an elementary school sent
a survey letter to each student’s parents
asking if voters in the school district would
support a tax increase to build a new
middle school.

Is this sample likely to be representative or
biased?
 The sample is biased. Parents of elementary
students who would be attending the new school
are more likely to support a new middle school
than would voters in general.

 It was convenient for the principal to survey
parents of students. In convenience sampling,
any easy method is used to choose the sample.
This is usually biased.

 Asking for responses to a survey is another
form of sampling that is often biased. People with
strong opinions are more likely to take the time to
respond to a survey than people in general.
Example 4.
Cassie wants to determine which brand
of athletic shoes is most popular with
U.S. middle school students. She
decides to stand near the entrance of
her school and keep a count of what
brands of shoes students are wearing
as they enter the school.
What sampling method is Cassie using?

Convenience Sampling

Is it likely to be representative or
biased? Why?

It is likely to be biased since she is
studying only students at her school.
The Moral of the Story:
Random sampling is important for
obtaining measures that accurately
describe the population being studied.
Convenience sampling and responses
to surveys involve a bias.

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