Unit 4 - STATISTICS
How do you predict the winner of an
election before the election takes
place?
In this lesson you will learn
how to collect data about a
population
by identifying a sample of
the population.
Let’s Review
Statistical questions are used to
gather data about a population.
How many texts do
middle school students
send in one day?
Core Lesson
That could take
a long time…
Core Lesson
By surveying a sample of the group, you can
make a generalization about the entire group.
Core Lesson
The population is the entire group
being studied.
A sample is part of the population being
surveyed.
Core Lesson
For example:
Predict the winner of the upcoming
presidential election
Population
Sample
American voters
Adults walking to work
Core Lesson
Another example:
Tracking migration pattern of birds
Population
Sample
A bird species
Tagged birds
In this lesson you have
learned how to collect data
about a population
by identifying a sample of
the population.
Guided Practice
Identify the population and sample in the
following survey:
To gauge students’ preference for a new
school mascot, the Student Council
President surveys her soccer team.
Population
Sample
Extension Activities
Answer the following questions.
1.You are buying ice cream for a party at your
school, in which 700 students will attend. How
would you use sampling to make a generalization
about students’ preferred ice cream flavors?
2.Why not survey all 700 students?
3.Describe the sample you would survey, and
explain why you chose that sample.
Quick Quiz
Identify the population and the sample:
1. A telephone survey is given to 2,000 randomly
selected families in order to predict the average
amount of money American families spend on
groceries each week.
2. To determine the number of students who
carry backpacks in school, Tina collects data on
the first 100 students who enter the building.
Let’s Review
Statistical measures are then used to
analyze that data.
How many texts do
middle school
students send in
one day?
Mean
Median
Mode
Range
Interquartile Range
Mean Absolute Deviation
If you had to order t-shirts for your entire
school, what sample would you choose to help
you predict how many
t-shirts of each size to order?
In this lesson you will learn how
to identify representative
samples by differentiating
between biased and unbiased
methods of sampling.
Let’s Review
The population is the entire group
being studied.
A sample is part of the population being
surveyed.
A Common Mistake
Not all samples will lead to
good predictions about an
entire population.
How tall
are 7th graders?
Core Lesson
Representative sample
prediction
based on
data
accurate
Valid inference
Core Lesson
Sampling method
Unbiased
Biased
Core Lesson
This sample comes from a
biased sampling method. It is
not representative of the
population.
Core Lesson
This sample comes from an
unbiased sampling method. It
is representative of the
population.
Core Lesson
Another example: Color of leaves in September
a) 100 fallen leaves collected from the ground
b) 100 leaves on tree branches
c) 50 fallen leaves and 50 leaves on branches
d) 50 fallen oak leaves and 50 oak leaves on
branches
Core Lesson
Unbiased sampling method
Representative sample
Valid inference
In this lesson you have
learned how to identify
representative samples by
differentiating between
biased and unbiased methods
of sampling.
Guided Practice
A market researcher wants to know how 18-25 year
old women spend their money. Which group would
be a representative sample?
a) 18-25 year old women at the mall
b) 18-25 men and women commuting to work
c) Women of all ages commuting to work
d) 18-25 year old women commuting to work
Extension Activities
In a complete paragraph, describe why the
following sampling method is biased, and suggest
an unbiased method.
You want to know your town’s favorite fast-food
restaurant. You randomly ask 30 people their
preference as they leave one of the fast-food
restaurants in town.
Quick Quiz
1. An ice-cream company wants to find out if its
ice cream is the favorite in the state. Which group
would be a representative sample?
a) Customers who visit their store
b) Employees of ice cream stores in the state
c) People at the state fair
d) Adults entering a gym in the capital city
Quick Quiz
2. Which is an unbiased sampling method for
predicting the type of payment most frequently used
at a grocery store?
Record the type of payment used by…
a) Students at the local high school
b) Every 10th customer entering the store
c) Every 10th customer in the cash-only line
d) Visa card holders
Random Sampling
 The “pick a name out of the hat”
technique
– Random number table
– Random number generator
Systematic Sampling
 All data is sequentially numbered
 Every nth piece of data is chosen
Stratified Sampling
 Data is divided
into subgroups
(strata)
 Strata are based
specific
characteristic
– Age
– Education level
– Etc.
Convience Sampling
 Data is chosen based on convenience
– BE WARY OF BIAS!
Voluntary Response Sampling
 A sample which includes only willing participants
Learning Task: Is It Valid?
STANDARD ADDRESSED IN THIS TASK
MCC7.SP.1. Understand that statistics can be used to
gain information about a population by examining a
sample of the population; generalizations about a
population from a sample are valid only if the sample is
representative of that population. Understand that
random sampling tends to produce representative
samples and support valid inferences
Complete each survey:
(you have 8 min)
 There are 5 surveys around the room.
 Quickly take each survey by placing your
sticker on the appropriate answer.
 When finished, sit quietly and wait for
instructions.
 What color is your hair? Brown ______ Blond ______
Red ______ Black _______
 Do you carry a cell phone? Yes______ No _________
 About how many text messages do you send in a day? 020 _____ 21-40 ______ >40 ______
 About how much time do you spend on homework? 0-15
min _____ 16-30 min _____ 31-45 min ______ 46-60
min _______ > 60 min ______
 What month were you born? Jan – March _____ April –
June _____ July-Sept. _____Oct-Dec ______
Using the survey results discuss the following vocabulary.
What is the population of your survey?
The population is the entire class. Population is the entire set of
items for which data can be collected.
Did your class perform a census or a survey? A census means you
ask everyone in the population. Survey means you ask a
representative sample of the population.
This is a census.
How would you describe your results from question 2 as a parameter
for the population? A parameter means you describe a
characteristic about the population based on your data.
Most seventh grade students carry a cell phone.
The manager of the Millcreek Mall wants to know the mean age of the people
who shop at the mall and the stores in which they typically shop. He hires
Barker Market Research Company to collect the data. Dennis works for the
Barker Market Research Company and has been put in charge of collecting data
for the Millcreek Mall. Dennis decides to interview 100 people one Saturday
because it is the mall’s busiest shopping day.
• Is the survey a sample or a census?
It is a sample.
•What is the population for this survey?
The population is everyone who comes to the mall.
•Is the sample size for the survey appropriate?
The sample size is too small for the population. The 100 people are not a
representative sample of the entire population.
In the summaries that follow,
determine if the sample
taken is representative of
the population without bias
shown:
ABC Family is a television channel that targets
families and young adults to view their station. ABC
Family regularly posts online poll questions to their
website. In 2010, ABC Family polled their viewers to
ask about airing Rated “R” movies after 8pm on their
channel. Almost 200,000 people responded, and 85%
of them disagreed with airing Rated “R” movies.
Solution: Voluntary Response- ABC Family is only asking from
data from their viewers, which may tend to be more
conservative since it is a family targeted television station.
Mrs. Jones wants to know how the 5th grade feels
about recess time. Mrs. Jones labels every student in
the 5th grade with a number. She then draws 50
numbers out of a hat and surveys these students.
Mrs. Jones determines that 5th graders would like
more recess time than they currently have.
Solution: This is a Simple Random Sample (SRS).
Mrs. Jones gave each child in the 5th grade the
same chance of being selected.
The City of Smallville wants to know how its
citizens feel about a new industrial park in town.
Surveyors stand in the Smallville Mall from 8am11am on a Tuesday morning and ask people their
opinion. 80% of the surveyed people said they
disagreed with a new industrial park.
Solution: This is convenience sampling. People at a
mall are “easy to reach”, but not every individual in
Smallville has an equal chance of being chosen. For
example, people that work and are not at the mall on
Tuesday morning have no chance of being chosen.
The National Rifle Association (NRA) took a poll
on their website, www.nra.com, and asked the
question, “Do you agree with the 2nd
Amendment: the Right to Bear Arms”? 98% of
the people surveyed said “Yes”, and 2% said
“No”.
Solution: This is voluntary response. The
NRA only asked people on their website,
which are more likely to be “pro 2nd
amendment.”
Biased or Unbiased?
The mayor surveys 100 supporters at a rally about the most important
issues to be addressed by the city council.
The principal sends out questionnaires to all of the students to find
out what kind of music students prefer at dances.
The owner of a record shop surveys only customers over the age
of 18 who shop at his store.
The teacher writes the name of each student on a piece of paper and
questions the students whose names are drawn.
A convenience store surveys customers one morning to determine what
products they may like the store to stock.
Each student’s name is written on a slip of paper and placed in a box. One slip of
paper is selected to determine the student to be the homeroom representative.
Biased or Unbiased?
A company randomly selects 500 customers from its database and
then surveys these customers to find out how they like their
service. Unbiased
A city-hall employ surveys 100 customers at a restaurant to learn
about the jobs and salaries of city residents.
Biased
A newspaper randomly chooses 100 names from a subscriber
database and then surveys those subscribers to see if they read
the restaurant reviews. Unbiased
Predicting Proportion:
sample piece
sample size
x
(prediction)
entire population
x = 2550 students
Example: A university has 30,600 students. In a
random sample of 240 students, 20 speak 3 or
more languages. Predict the number of students at
the university that speak 3 or more languages.
There are 4500 elk located on a preserve in
Colorado. A biologist thinks that the herd may
be infected with parasite. She does a random
sample of 50 elk. If she discovers that 8 of the
sample is infected. Predict how many elk the
biologist can expect to be infected.
720 elk are infected
A factory produces 150,000 light bulbs per day. The
manager estimates that less than 1,000 defective
bulbs are produced each day. In a random sample of
250 light bulbs, there are 2 defective bulbs.
Determine if the manager's estimate is likely to be
accurate. Explain.
His estimate is incorrect. There are at
least 1200 defective bulbs each day.
A middle school has 2,500 students. Morgan
interviewed 75 students about their library habits. She
found that 45 of the students checked out a book
weekly. Predict the number of students likely to check
out books weekly.
1500 students
Yes. 56 students have traveled.
Zack chooses a random sample of 50 out of 400
students. He finds that 7 of them have traveled to
a foreign country. Zack claims that more than 50
of the 400 students have traveled to a foreign
country. Do you agree with his answer? Explain.