Name:_________________________________
M5L8
Accordino-Math 7
Date:_________
Period:________
Lesson 8: Populations, Samples, and What
Makes a Random Sample?
Bellringer
Be prepared to discuss which of the following are considered fair?
1) All the girls get candy.
2) All the athletes do not have to do their homework.
3) Every fifth student in the door gets a prize.
4) Mrs. A chooses your name out of the bucket to answer the next question?
Name:_________________________________
M5L8
Date:_________
Accordino-Math 7
Period:________
Lesson 8: Populations, Samples, and What Makes a Random
Sample?
Notes
Let’s Think:
What is a population?
What is a sample?
What is bias?
In a previous lesson we created a simulation to help estimate the probability of having two boys and one girl in a
given family of three children. How does the estimated probability compare to the actual probability of this class?
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How could we get a better estimation of the probability of having two boys and one girl right here in Sauquoit, NY?
Population:
Sample:
Biased Sample:
What makes a sample representative of the whole population?
Name:_________________________________
M5L8
Accordino-Math 7
Date:_________
Period:________
Exercise 1: Random or Biased?
Indicate which of the following would result in a random sample and which would result in a biased sample.
Explain your reasoning for each choice.
a.
Use a pattern, such as selecting every fourth person who enters the cafeteria.
b.
Use a method such as drawing names from a hat, where everyone has an equal chance of being selected.
c.
Let people volunteer to take a survey.
d.
Choose people who are easy to reach, such as the students who happen to be in the cafeteria when you
are available to give surveys.
e.
Choose people as a group, such as all students who play soccer.
f.
Divide the population into groups, such as by grade level, and randomly select people from each group.
Exercise 2: Representative Sample?
Indicate whether the following are random samples from the given population, and explain why or why not.
g.
Population: All students in school; sample includes every fifth student in the hall outside of class.
h.
Population: Students in your class; sample consists of students that have the letter “s” in their last
name.
i.
Population: Students in your class; sample selected by putting their names in a hat and drawing the
sample from the hat.
j.
Population: People in your neighborhood; sample includes those outside in the neighborhood at 6:00
p.m.
k.
Population: Everyone in a room; sample selected by having everyone toss a coin, and those that result in
heads are the sample.
Exercise 3: Using Random Samples
Carla has a list of all 432 students in her middle school. She writes each of their names on a slip of paper and pulls
30 names out to survey about their favorite holiday.
a. How many students are in Carla’s sample?
b. How many students are in Carla’s population?
c. If 17 students say they like Christmas, 10 Halloween, 2 Hanukah, and 1 does not observe holidays. How many
students could you estimate prefer Halloween out of the entire middle school population?
Name:_________________________________
M5L8
Date:_________
Accordino-Math 7
Period:________
Homework: None of the questions tonight are multiple choice. Consider each option separetly in the
context of the question.
1.
2.
3.
Would any of the following provide a random sample of letters used in text of the book Harry Potter and the
Sorcerer’s Stone by J.K. Rowling? Explain your reasoning.
i.
Use the first letter of every word of a randomly chosen paragraph.
ii.
Number all of the letters in the words in a paragraph of the book, cut out the numbers, and put them in
a bag. Then, choose a random set of numbers from the bag to identify which letters you will use.
iii.
Have a family member or friend write down a list of their favorite words, and count the number of times
each of the letters occurs.
For each of the following questions describe how you might collect data to answer the question.
i.
Where should the eighth-grade class go for their class trip?
ii.
What is the average number of pets per family for families that live in your town?
iii.
If people tried a new diet, what percentage would have an improvement in cholesterol reading?
iv.
What is the average grade point of students who got accepted to a particular state university?
v.
What is a typical number of home runs hit in a particular season for major league baseball players?
The teachers in your school are asked to send four students to the cafeteria after announcements to represent
the class.
Teacher 1
Teacher 2
Teacher 3
Puts the names of all the girls in a
box and chooses two without
looking. Then she does the same
with the boys’ names.
Sends the four closest students to
the door.
Puts all students’ names in a box at
the same time and pulls four out
without looking.
a. Compare the selection methods. Do you think each one creates a random or biased sample? Which is more
likely to be representative? Explain.
4.
You and a friend decide to conduct a survey at your school to see whether students are in favor of a new dress
code policy. Your friend stands at the school entrance and asks the opinions of the first 100 students who
come to campus on Monday. You obtain a list of all students at the school and randomly select 60 to survey.
Your friend finds 34% of his sample in favor of the new dress code policy, but you find only 16%. Which do
you believe is more likely to be representative of the school population? Explain your choice.
5.
Veronica randomly surveyed a group of students to find out how they arrived at school each day; her findings
are recorded in the table below. Using the data from the table, estimate how many students drive to school if
the total school population is 500 students.
# of Students
Walk
8
Car
7
Bike
3
Bus
42
Name:_________________________________
Accordino-Math 7
M5L8
Date:_________
Period:________
Lesson 8: Populations, Samples, and What
Makes a Random Sample?
Exit Ticket
Mrs. A has 76 wonderful seventh graders that she teaches this year. She took a random survey of 20 students and
found that seven students like twizzlers, 12 like jolly ranchers, and one does not eat sweets.
a. How many students are in Mrs. A’s sample?
b. How many students are in Mrs. A’s population?
c. Using Mrs. A’s sample, how many students would you estimate prefer jolly ranchers out of the entire seventh
grade?