CHAPTER
11
Data Analysis
GET READY
614
Math Link
616
11.1 Warm Up
617
11.1 Factors Affecting Data Collection
618
11.2 Warm Up
625
11.2 Collecting Data
626
11.3 Warm Up
635
11.3 Probability in Society
636
11.4 Warm Up
649
11.4 Developing and Implementing a Project Plan 650
s
Math Link: Wrap It Up!
654
Graphic Organizer
655
Chapter 11 Review
656
Key Word Builder
660
Chapter 11 Practice Test
661
Challenge
663
Chapters 8–11 Review
664
Answers
671
Name: _____________________________________________________
Date: ______________
Get Ready
Measures of Central Tendency
sum of items
number of items
example: In the data set 1, 3, 4, 1, 5, 2, 4, 4, the mean is 3:
1 + 1 + 2 + 3 + 4 + 4 + 4 + 5 24
=
=3
8
8
Mean: what most people call the average. Mean =
●
lowest to highest
Median: the middle number in a set of data that has been arranged in ascending order
● example: 43, 43, 45, 46, 47 has an odd number of data values.
The middle number is 45, so 45 is the median.
● example: 1, 1, 2, 3, 4, 4, 4, 5 has an even number of data values. The median is halfway
3+ 4
= 3.5
between the two middle numbers, 3 and 4. Median =
2
Mode: the number that appears the most often in a set of data.
● example: In 1, 1, 2, 3, 4, 4, 4, 5, the mode is 4.
● A data set can have more than 1 mode.
● example: In 1, 3, 3, 6, 6, 10, the modes are 3 and 6.
1.
Find the mean, median, and mode.
a) 1, 3, 6, 2, 8, 5, 15, 15, 8
Mean =
=
sum of values
number of values
1 + 3 + 6 + 2 + 8 + 5 + 15 + 15 + 8
=
=
Ascending order:
Median =
Mode =
614
MHR ● Chapter 11: Data Analysis
b) 4.3, 4.5, 4.2, 5
Name: _____________________________________________________
Date: ______________
Calculating the Range
The range tells you about the spread of the data.
● Range = highest value – lowest value
● example: 1, 1, 2, 3, 4, 4, 4, 5
Highest value = 5; lowest value = 1. The range is 5 – 1 = 4.
2.
Find the range.
a) 9, 8, 8, 3, 7
b) 16, 11, 7, 29, 31, 24, 18, 18, 18
Range = highest value – lowest value
=
–
=
Representing Data
Circle graphs are best for comparing parts
of a whole using percents.
De Re
lic d
iou
s
De
lic
Go
Fu
iou n
s
Jo
go nal
M d
ac
int
os
h
Varieties of Apples Sold
ji
60
50
40
30
20
10
0
lde
Number of Apples
You can show data using graphs.
Bar graphs are best for comparing data
across different groups.
Variety
Line graphs are best for showing changes
in data over time.
Number of T-Shirts
Pictographs are best for comparing data
that can be easily counted.
50
40
30
20
10
0
T-Shirt Sales
1 2 3 4 5 6 7
Week
Truong recorded the water flow from 3 taps on a line graph.
a) Which tap flows the fastest?
b) What is the approximate water flow in 2 min from Tap B?
Volume (L)
3.
Water Flow From Three Taps
A
45
40
35
30
25
20
15
10
5
0
1
2
3
4
Time (min)
B
C
Get Ready ● MHR 615
Name: _____________________________________________________
Date: ______________
Math Link
Protecting and Managing Wildlife
Elk Island National Park in Alberta is home to many ungulates.
An ungulate is a mammal with hooves, such as plains bison,
wood bison, moose, deer, and elk.
The table shows data about the ungulates in the park.
1.
Display the data on a bar graph.
Then, display the data on a pictograph.
For a bar graph:
‰ Choose a scale for the y-axis.
‰ Title and label both axes.
‰ Plot the categories along the x-axis.
‰ Draw bars for each ungulate.
‰ Add a title.
Ungulate
Approximate Total
Park Count
(2007 Fall Count)
Plains bison
425
Wood bison
400
Elk
605
Moose
300
Deer
558
For a pictograph:
‰ Choose symbols for each category.
‰ Provide a key or a legend.
‰ Add a title.
‰ Complete the graph.
y
x
2.
Which ungulate has the largest population?
3.
a) The park has an area of 194 km2.
What is the mean number of elk per
square kilometre? Round your answer
to the nearest whole number.
number of elk
=
area
=
616
/km2
MHR ● Chapter 11: Data Analysis
b) What percent of the ungulate population do
bison represent? Round your answer to the
nearest percent.
number of bison
× 100
total number of ungulates
Name: _____________________________________________________
Date: ______________
11.1 Warm Up
1.
The graph shows categories of books the Wong
family signed out from the library.
a) Approximately how many books in total did the
Wong family sign out?
b) Which category of book did the Wong family
sign out most often?
2.
The circle graph is another way to show the categories of books the
Wong family signed out from the library.
a) What percent of the books are Adventure or Sports?
b) Is it possible that the Wong family signed out books from categories
other than the ones shown?
Circle YES or NO. Give 1 reason for your answer.
_____________________________________________________________________________
3.
The mean of 40, 50, and 60 is
.
4.
A school has 400 students. If 40 students were surveyed, what percent of the school was surveyed?
Sentence: _______________________________________________________________________
11.1 Warm Up ● MHR 617
Name: _____________________________________________________
Date: ______________
11.1 Factors Affecting Data Collection
Link the Ideas
When you do a survey, influencing factors can affect the data you collect:
Literacy Link
A survey collects
opinions and/or
information.
●
bias: Does the question seem to show that one thing is better than another?
●
use of language: Can people understand the question?
●
ethics: Does the question ask about inappropriate things?
●
cost: Does the study cost too much?
●
time and timing: Is the survey being done at the right time?
How long does it take to do the survey?
●
privacy: Do people have the right to refuse to answer?
Are the responses kept a secret?
●
cultural sensitivity: Could the question offend people from different cultural groups?
Literacy Link
Ethics involve
judgments of right and
wrong. For example,
cheating on a test is
ethically wrong.
Working Example 1: Identify Factors Affecting Data Collection
Check each situation for influencing factors.
Give 1 reason for each factor you find.
a) A salesperson stands in front of a display of toothpaste.
He asks every person buying toothpaste this question:
What is your favourite brand of
toothpaste? For what reason(s)?
Solution
Ask yourself, “Does the question seem to show that one kind of toothpaste is better than another?”
Circle YES or NO.
There is no bias.
By standing in front of a toothpaste display, the salesperson can survey people who are buying
toothpaste.
Asking questions to gather information.
618
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
b) A company sends free samples of sunscreen to every home in fall and winter.
A survey asks people if they would use the sunscreen again.
Solution
Ask yourself, “Is this question being asked at the right time of year?” Circle YES or NO.
People likely wear
sunscreen during the fall and winter than
(more or less)
during the summer.
So, fall and winter
the best time for testing sunscreen.
(are or are not)
Asking people if they will use the product again assumes they
use it.
(did or did not)
This may confuse people. The language is unclear.
c)
A grocery store employee does a telephone survey of people living within 10 km of the store.
She asks what type of red meat people prefer.
Solution
Ask yourself, “Could this question offend some people?” Circle YES or NO.
The question is biased. It assumes that all people eat
Red meat is not acceptable to some people.
This may be a sensitive question for some people.
meat.
d) A sales representative does a telephone survey.
As she asks the question, the person receiving the call says,
“I am not interested, thank you.”
The sales representative responds, “Why not? Your input
provides useful information.”
She begins to repeat the survey question.
Solution
Ask yourself, “Does the person have the right to refuse to participate?”
Circle YES or NO.
The sales representative
respect the person’s right to refuse to participate
(did or did not)
in the survey. Responses obtained under pressure may not truly represent the person’s opinion.
11.1 Factors Affecting Data Collection ● MHR 619
Name: _____________________________________________________
e)
Date: ______________
Your school is under construction and is dusty and dirty.
A survey is conducted about the environmental health of your school.
The survey is done every 4 years.
Solution
Ask yourself, “Is the survey being conducted at a good time?” Circle YES or NO.
This survey is poorly timed.
The school is under construction so the results will be unfair.
f)
A salesperson sets up an online survey.
The survey offers a free MP3 file download to everyone who completes the survey.
The company has not bought the rights to the song.
An ethical survey
is honest and fair.
Solution
Ask yourself, “Is the survey ethical?” Circle YES or NO.
The download is being stolen, which is wrong. Also, giving a reward for doing a survey is not ethical
because the reward may change the way people respond.
Kelly is selling school shirts to students in grades 8 to 12.
She has 2 different kinds of shirts. She wants to know which shirt students like better.
She asks the first 10 grade 12 students who come to school this question:
Which one of these 2 shirts would you buy?
The poster shows the results.
Over 80% of students at
Central High will buy Shirt B.
A: $29.95
B: $49.95
a) Is the survey fair? Circle YES or NO.
Give 2 reasons why or why not.
●
__________________________________________________________________________
●
__________________________________________________________________________
b) What is 1 way to improve the survey?
___________________________________________________________________________
620
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
Working Example 2: Write Survey Questions Free of Influencing Factors
A steel mill company conducts a survey about putting a new mill
in a small community.
Influencing factors affect
how data are collected or
the answers people give.
The proposed mill will produce 250 jobs and
economic benefits for your community. Are
you in favour of having a forward-thinking
steel mill in your community? YES NO
a) What parts of the question help the steel mill get positive responses?
Solution
Ask yourself, “What parts of the article make the mill look like a good idea?”
The first part says jobs would be
.
(created or taken away)
Also, the question says the mill is “forward thinking.”
The survey is biased in favour of the mill.
b) Rewrite the question so it is free of influencing factors.
has influencing factors
Solution
Are you in favour of having a steel mill in your community?
For each question, list the influencing factors. Then, rewrite the question.
a) Daniel is studying the population of polar bears in Hudson Bay. He writes this question:
Do you think the senseless slaughter of polar bears should be stopped? YES NO
Influencing factor: ___________________________________________________________
Rewrite question: ____________________________________________________________
___________________________________________________________________________
b) A recent study shows that 45% of Canadians shop on the Internet.
Amy writes this question for a survey: What do you buy online?
Influencing factor: ___________________________________________________________
Rewrite question: ____________________________________________________________
___________________________________________________________________________
11.1 Factors Affecting Data Collection ● MHR 621
Name: _____________________________________________________
Date: ______________
Check Your Understanding
Communicate the Ideas
1.
Hakim says a survey can be biased without telling a lie.
Write a survey question about the types of music people like. Make it biased, but with no lies in it.
_______________________________________________________________________________
_______________________________________________________________________________
2.
A community uses a survey to decide whether to build a hockey arena or a swimming pool.
Write the letter of the situation beside the influencing factor that matches it.
a) The survey question is, “Do you want a fun-filled winter?
Circle hockey as your choice!”
bias
ethics
b) The survey is handed out at a swim meet.
cost
c) The community hires a survey company for $20 000.
This cost is not in the budget.
time/timing
Practise
3.
Each situation shows bias.
Underline the part that needs to be changed to remove the bias.
a) Ask hockey players if they are willing to pay higher registration fees for hockey.
b) Ask new motorcyclists if helmets should be mandatory.
c) Ask forestry workers if more money should be spent on fighting forest fires.
4.
Underline the inappropriate part of each situation.
a) A survey asks how much parents earn in 1 year.
b) Only teachers are asked their opinion about a new school name.
c) The Arts Council is surveyed about the importance of art classes in schools.
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MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
5.
Date: ______________
Rewrite each survey question so there are no influencing factors.
a)
b)
Do you like to watch hockey, the only great
sport?
YES NO
__________________________________________
Most people choose chocolate, but what is
your favourite flavour of ice cream?
__________________________________________
__________________________________________
__________________________________________
c)
A recent survey shows that 42% of teens
use the Internet to watch TV. What TV
shows do you watch most often online?
__________________________________________
__________________________________________
Apply
6.
Write a survey question for each situation. Who would you ask to participate in the survey?
a) Which sport teens like best
Question : ____________________________________________________________________
_____________________________________________________________________________
Participants: __________________________________________________________________
b) If price or brand is more important when buying a cell phone
Question : ____________________________________________________________________
_____________________________________________________________________________
Participants: __________________________________________________________________
c) Which Internet site people trust most to give them correct information
Question : ____________________________________________________________________
_____________________________________________________________________________
Participants: __________________________________________________________________
11.1 Factors Affecting Data Collection ● MHR 623
Name: _____________________________________________________
7.
Date: ______________
Rewrite each survey question so that it collects more helpful data.
a)
__________________________________________
If you are a juice drinker, would you consider
switching to Crystal Juice?
YES NO
__________________________________________
__________________________________________
b)
Which of the following cough medicines
have you tried?
__________________________________________
__________________________________________
__________________________________________
c)
Are you satisfied with your Internet access?
Circle one response.
A Excellent
B Good
C Poor
__________________________________________
__________________________________________
__________________________________________
Math Link
One of the ways to save endangered species is to set aside land for them.
You survey a sample of Canadians.
Write 3 fair survey questions to find out who is in favour of creating National Parks for endangered
species.
Question #1: Find out if Canadians think the government should create National Parks.
___________________________________________________________________________________
Question #2: Find out if Canadians think the cost of the land is important to the decision.
___________________________________________________________________________________
Question #3: Find out if Canadians are worried about people who might be affected, such as those living
on the land.
___________________________________________________________________________________
Test your questions with a classmate to see if they are clear and useful.
624
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
11.2 Warm Up
1.
Sometimes we survey only a small number of people when we need information about the
whole group. Give 1 reason why surveying everyone might be difficult.
________________________________________________________________________________
2.
Fill in the blanks with “more” or “less.”
The
people who are surveyed, the
(more or less)
accurate the results will be.
3.
(more or less)
Evaluate.
a) 10% of a group of 350
10% of 350
= 0.1 × 350
b) 25% of a group of 788
To change a percent to a
decimal, divide by 100.
=
4.
Calculate the percent of the population each situation represents.
a) 12 out of a population of 240 people
12
=
240
← decimal
=
← percent
This is
% of the population.
b) 90 out of a population of 450 people
This is
5.
% of the population.
Starting at 1, list every seventh number between 1 and 100.
________________________________________________________________________________
11.2 Warm Up ● MHR 625
Name: _____________________________________________________
Date: ______________
11.2 Collecting Data
Link the Ideas
Working Example 1: Identify the Population
population
● all of the individuals in the group being studied
● example: the population in an election is all the voters
sample
● a group of individuals chosen from the population
● example: 100 voters chosen from each province or territory is a sample
Identify the population for each situation.
Would you survey a sample or the whole population? Why?
a) A bike store owner wants to find out which brand of mountain
bike her customers prefer.
Solution
●
●
The population is
.
(the store’s customers or high school students)
Ask yourself, “Would it be possible to survey every customer?” Circle YES or NO.
It depends on the size of the store.
A small store might survey all of its customers.
A large store would likely survey
of its customers.
(a sample or the whole population)
It would be time-consuming and expensive for a large store to survey all the customers.
b) The government of Canada wants to know how many high school students have Internet access.
Solution
●
Ask yourself, “Who does the government want to know about?”
The population is
in Canada.
(high school students or people)
●
Ask yourself, “Would it be possible to survey every high school student in the country?”
Circle YES or NO.
It would make sense to survey
because it would take too much time to
(a sample or the whole population)
find all the high school students in Canada.
626
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
c)
Date: ______________
A basketball coach needs to find out if the team wants to go to an out-of-town tournament.
Solution
●
Ask yourself, “Who does the coach need to ask?”
The population is
●
.
Ask yourself, “Would it be possible to ask each person on the team?” Circle YES or NO.
It would make sense to survey
because the coach should get
(a sample or the whole population)
everyone’s input.
For each situation, state
● the population
● whether you would survey the whole population or a sample
● your reason for surveying the population or a sample
a) A store owner wants to find out if his customers are happy with the service.
The population is
. I would survey the
because
(whole population or sample)
__________________________________________________________________________.
b) The Royal Garden Restaurant wants to know which dish customers like best.
The population is
. I would survey the
because
(whole population or sample)
__________________________________________________________________________.
c) Stefan wants to find out if teachers in Canada prefer to wear glasses or contact lenses.
The population is
. I would survey the
because
(whole population or sample)
__________________________________________________________________________.
11.2 Collecting Data ● MHR 627
Name: _____________________________________________________
Date: ______________
Working Example 2: Identify a Sample
There are several types of samples.
convenience sample
● choose individuals from the population who are easy to find or talk to
voluntary response sample
● invite the whole population to participate
Voluntary means you can choose
whether to participate.
random sample
● choose a specific number of individuals from the whole population
● random means that each individual has an equal chance of being chosen
● you can use data from a random sample to make predictions about the population
● there are 2 types of random samples:
stratified sample
● First, divide the population
into different groups.
● Then, choose the same
percent of members from
each group.
systematic sample
● Choose individuals at fixed
intervals (such as every fifth
person) from an ordered list
of the whole population.
For each situation, describe how you could choose the sample.
What type of sample would work best?
a) A teacher wants to get feedback about a school dance from her class of 30 students.
She plans to ask 5 students.
Solution
The teacher could put all the students’ names in a hat and choose 5 of them. This is a random sample.
b) A company wants to see if its 3000 employees would use a fitness centre.
It plans to survey 300 employees.
Solution
The company plans to survey
out of 3000 employees.
It could survey every tenth person on a list of employees.
This is a systematic sample.
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MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
c)
Date: ______________
A company is deciding whether to open a new store in Camrose, Alberta.
The company surveys people in Camrose and 3 nearby towns.
The table shows the population of each location.
Town
Population
Camrose
16 000
Bashaw
825
Tofield
1 876
Daysland
876
Solution
The company could survey 25% of the population in each
This is a stratified sample.
.
d) A company mails a survey to all adults in a town.
Everyone is asked to mail their responses back.
Solution
Since every
voluntary response sample.
is invited to participate in the survey, this is a
This sample may not represent the population.
Only those who are
will respond.
(interested or not interested )
e)
A restaurant owner wants to know his customers’ favourite pizza topping.
He surveys every customer who orders pizza between 5:00 p.m. and 10:00 p.m.
Solution
Is this a random sample? Circle YES or NO.
Ask yourself, “Does every customer
have a chance of being surveyed?”
This is a convenience sample. Only customers who order pizza between those times are surveyed.
11.2 Collecting Data ● MHR 629
Name: _____________________________________________________
Date: ______________
1. For each situation, what type of sample would you use?
● convenience
● voluntary
● random
● systematic
● stratified
How would you choose the sample?
a) A school librarian asks students which new fiction books she should order for the library.
There are 424 students in the school.
Type of sample:
.
Choose the students by ______________________________________________________
_________________________________________________________________________
b) A company plans to do a telephone survey to find out if people want a new art gallery.
There are 800 000 people in the city.
Type of sample:
Choose the people by _______________________________________________________
_________________________________________________________________________
2. Identify the type of sample in each case.
a) A coach puts the names of all of the basketball players into a hat.
Then, he draws 1 name for a free basketball.
b) A company sends a questionnaire to every 9th person on an alphabetical list.
c) The student council invites all students to suggest ideas for activities.
d) The school principal asks each teacher to have 20% of their class answer a questionnaire.
630
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
Check Your Understanding
Communicate the Ideas
1.
Kris decides to survey everyone in Canada to find out which bands are the most popular.
a) Is this a survey of a sample or a population? Circle SAMPLE or POPULATION.
b) Do you agree with his method? Circle YES or NO.
Give 1 reason for your answer.
____________________________________________________________________________
____________________________________________________________________________
2.
Kim and Scott want to know how many people took public transit to a concert.
There are 18 000 people at the concert.
Kim:
I plan to ask the
first 20 people
who arrive.
Scott:
I plan to ask
the first
200 people.
a) Whose sample best represents the population? Circle KIM or SCOTT.
Give 1 reason for your choice.
____________________________________________________________________________
____________________________________________________________________________
b) What other type of sample would give more accurate results?
Give 1 reason for your answer.
correct
____________________________________________________________________________
____________________________________________________________________________
3.
Describe the difference between surveying the population of British Columbia and surveying a
sample of people who live there.
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
11.2 Collecting Data ● MHR 631
Name: _____________________________________________________
Date: ______________
Practise
4.
5.
Write the matching letter beside the type of sample that should be used for the situation.
a) A large school surveys 20% of the students from each grade.
random
b) The school store asks the first 20 customers
what type of juice they like the best.
voluntary
c) A company picks every 100th person in a phone book.
convenience
d) In a class of 40 students, each student is assigned a number.
The teacher picks 5 numbers from a hat.
stratified
e) Students are asked to do an online survey if they wish.
systematic
Write the population in each situation. Would you survey the whole population or a sample of the
population? Give 1 reason for your answer.
a) The principal wants to know if teachers and students are in favour of school uniforms.
Population:
because _________________________________
I would survey
(sample or population)
_____________________________________________________________________________
b) An electronics store wants to know if its customers are happy with the repair department.
Population:
I would survey
because _________________________________
_____________________________________________________________________________
c) The town wants to know if buses are needed for people with disabilities.
Population:
I would survey
because _______________________________________________________
______________________________________________________________
632
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
Apply
6.
For each situation, would you survey the population or a sample?
Give 1 reason for your answer.
a) To determine the air quality in hospitals in Edmonton, Alberta:
I would survey ________________________ because ________________________________
____________________________________________________________________________.
b) To find out the plans of grade 9 students after they graduate from high school:
I would survey ________________________ because ________________________________
____________________________________________________________________________.
c) To test the quality of parachutes:
I would survey ________________________ because ________________________________
____________________________________________________________________________.
d) To test the quality of bike tires:
I would survey ________________________ because ________________________________
____________________________________________________________________________.
7.
Kristi wants to create a menu for a family picnic.
Her family includes 20 adults, 8 teens, and 12 children.
She only has time to talk to 10 people. How should she choose her sample?
Explain.
_______________________________________________________________________________
_______________________________________________________________________________
8.
Erin plans to survey her friends to determine the average number of children per household in
Canada.
a) Is this a random sample? Circle YES or NO.
b) Give 1 reason for your answer.
____________________________________________________________________________
____________________________________________________________________________
11.2 Collecting Data ● MHR 633
Name: _____________________________________________________
9.
Jason wants to ask each student who enters the cafeteria
the following question.
Date: ______________
What is your favourite paint colour for
the cafeteria walls? ________
a) What is the population?
b) What is the sample?
c) Will his results accurately represent the population? Circle YES or NO.
Give 1 reason for your answer.
_____________________________________________________________________________
Math Link
Write a research question about an endangered animal.
a) What endangered animal will you research?
b) Find the size of the animal’s population before it was endangered.
What is the population now?
c)
What is 1 reason for the decline of the population?
_______________________________________________________________________________
_______________________________________________________________________________
d) Write a question that you can research about the endangered animal.
_______________________________________
_______________________________________
Research Question: What are the population
trends for beluga whales in Canada?
_______________________________________
To answer your question, find data from studies and
surveys that other people have done.
e)
What sampling method did researchers use
to collect the data?
Beluga whale, Somerset
Island, Nunavut
Give 1 reason for your answer. ______________________________________________________
_______________________________________________________________________________
634
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
11.3 Warm Up
1.
Explain what probability means by using a weather forecast.
_______________________________________________________________________________
2.
Find the probability. Write your answer as a fraction, a decimal, and a percent.
a) choosing a heart from a full deck of cards
P(hearts) =
b) spinning a B on the spinner
number of favourable outcomes
total number of outcomes
A
A
B
=
3.
B
C
52
=
← decimal (13 ÷ 52)
=
← percent (multiply by 100)
Find the mean, median, and mode of each set of data.
a) 13, 10, 9, 13, 8
Mean =
sum of items
number of items
Median:
Write the numbers in order:
8, 9,
b) 111, 132, 100, 123, 111, 100
Mean:
Median:
Add the two middle
numbers and divide by 2.
, 13, 13
The median is
The mode is
Mode:
11.3 Warm Up ● MHR 635
Name: _____________________________________________________
Date: ______________
11.3 Probability in Society
Link the Ideas
Working Example 1: Use a Sample to Make a Prediction About the Population
a) The grade 12 students in 5 of 7 high schools recorded their eye colour.
A total of 2300 grade 12 students were surveyed.
The table shows the results.
Eye Colour
Total
Brown
1656
Blue
483
Green
115
Other
46
Predict how many of the 7200 students at a college will have brown eyes.
Show your thinking.
Solution
Of the 2300 high school students surveyed,
1656
× 100
2300
= 0.72 × 100
%
Step 2: Calculate 72% of 7200.
0.72 × 7200
=
Step 3: Write a prediction statement.
Approximately
636
students at the college will have brown eyes.
MHR ● Chapter 11: Data Analysis
To predict is to tell
what might happen.
students have brown eyes.
Step 1: Find the percent of students who have brown eyes:
=
Literacy Link
Name: _____________________________________________________
Date: ______________
b) Is your prediction reasonable? Explain why or why not.
Solution
No, not necessarily.
There is an assumption that the high school sample represents
the college population.
The sample represents the grade
Literacy Link
An assumption is
something taken
for granted, as if
it were true.
population.
The sample may not represent the college student population. Students may come from other high
schools, provinces, territories, or countries. So, the sample is a biased sample.
The prediction may be
for the college population.
(valid or not valid )
biased sample
● does not represent the population
● can make survey results inaccurate or not valid
c)
Rewrite a more accurate prediction statement.
Solution
If the student population in the high schools and college are
,
(different or similar)
approximately 5200 college students have
A total of 2300 grade 12 students were surveyed.
Predict how many college students have blue eyes.
Step 1: Find the percent of students who have blue eyes.
eyes.
Eye Colour
Total
Brown
1656
Blue
483
Green
115
Other
46
Step 2: Calculate the number of 7200 college students who have blue eyes.
Step 3: Write a prediction statement.
_____________________________________________________________________________
11.3 Probability in Society ● MHR 637
Name: _____________________________________________________
Date: ______________
Working Example 2: Avoid Making a False Prediction
Mr. Krutz gave an assignment worth 30 marks.
After marking the first 5 papers, he was worried that the
students did not understand the assignment.
He predicted that most of the students would not do well.
a) Use Mr. Krutz’s sample of marks to predict
the class’s average mark.
Write the average mark as a percent.
Solution
Use the measures of central tendency.
Mean =
=
mean, median,
and mode
sum of items
number of items
20 + 15 + 18 +
=
+
5
5
=
The mean is
.
The median is the middle number.
First, write the numbers in order: 15, 18, 18, 19,
. The median is
The mode is the number that appears the most often. The mode is
.
.
The mean, median, and mode for the sample are 18.
Average mark =
18
× 100
30
= 0.6 × 100
=
%
Based on the sample statistics, I predict the average mark as a percent is
638
MHR ● Chapter 11: Data Analysis
.
Name: _____________________________________________________
Date: ______________
b) The scores for all 30 students in the class are:
20 15 18 19 18 16 17 23 24 30
22 24 21 20 24 25 19 24 15 28
27 28 22 24 19 13 28 22 24 20
Why did Mr. Krutz’s sample lead him to make a false prediction?
Literacy Link
A false prediction is an
incorrect prediction.
Solution
The mean, median, and mode for all the marks are
● mean = 21.6333…
● median = 22
Which mark appears
●
the most often?
mode =
Mr. Krutz assumed that the sample of the first
This is FALSE.
papers was representative of the whole class.
The mean score in the sample is 60%.
The mean score in the class is approximately
21.63
× 100
30
=
%
The mode written as a percent is
24
× 100
30
= 0.8 × 100
=
%
Mr. Krutz may have used too small of a sample to make his prediction.
The sample
represent the population.
(does or does not)
11.3 Probability in Society ● MHR 639
Name: _____________________________________________________
Look at Mr. Krutz’s students’ marks.
20 15 18 19 18 16 17 23 24 30
22 24 21 20 24 25 19 24 15 28
27 28 22 24 19 13 28 22 24 20
Date: ______________
last 5 papers
a) Predict the average mark if Mr. Krutz had marked the last 5 papers first.
Use the measures of central tendency.
Mean =
sum of items
number of items
The mean is
.
Median:
Write the numbers in order:
The median is
The mode is
.
.
Average mark:
Prediction: _________________________________________________________________
b) Do these marks give a more reasonable prediction of the class average? Circle YES or NO.
Give 1 reason for your answer.
__________________________________________________________________________
640
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
Working Example 3: Make a Decision Based on Probability
A youth association surveys 400 members about their favourite activity.
There are 100 members in each of 4 different groups.
The table shows the survey results.
Group
Swimming
Rock Climbing
Watching Movies
Bowling
Total
Red
14
9
40
37
100
Blue
11
19
59
11
100
Green
27
12
57
4
100
Yellow
13
24
44
19
100
a) What is the theoretical probability that a member of any group will choose swimming?
Based on your answer, predict how many of the 400 members will choose swimming.
Solution
Literacy Link
The members have an equal chance of choosing any 1 of the
4 activities.
P(swimming) = number of favourable outcomes
total number of outcomes
=
1
or
4
theoretical probability
The chance of an event happening.
Theoretical probability
# of favourable outcomes
=
total # of outcomes
%
The theoretical probability that a member of any group will choose swimming is
Predict how many of the 400 members will choose swimming.
.
1
× 400
4
400
=
4
=
I predict that
members will choose swimming.
b) What assumptions did you make?
Solution
●
Every activity has an
●
(equal or unequal)
Members have the same interest in each activity.
chance of being selected.
11.3 Probability in Society ● MHR 641
Name: _____________________________________________________
Date: ______________
Use the results in the table to predict the probability that a member will choose swimming.
c)
Group
Swimming
Rock Climbing
Watching Movies
Bowling
Total
Red
14
9
40
37
100
Blue
11
19
59
11
100
Green
27
12
57
4
100
Yellow
13
24
44
19
100
Solution
Literacy Link
Use experimental probability to help make the prediction.
experimental probability
The chance of an event
happening based on the
results of an experiment.
number of favourable outcomes
total number of outcomes
14 + 11 + 27 + 13
=
400
P(swimming) =
=
Write
Experimental probability
# of favourable outcomes
=
total # of outcomes
400
65
as a percent.
400
65
× 100
400
= 0.1625 × 100
=
%
The experimental probability that a member will choose swimming is
%.
d) Compare your answers for parts a) and c). Explain any differences.
Solution
25%
16.25%
(> or <)
The
< means less than
> means greater than
probability is greater than the
(theoretical or experimental)
probability.
The
(theoretical or experimental)
probability shows a truer picture of the youths’ interests.
(theoretical or experimental)
642
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Group
Red
Blue
Green
Yellow
Date: ______________
Swimming
Rock Climbing
Watching Movies
Bowling
Total
14
11
27
13
9
19
12
24
40
59
57
44
37
11
4
19
100
100
100
100
a) What is the experimental probability that a member will choose each of the following?
Watching Movies:
Bowling:
b) Pretend you are a youth coordinator planning the activities.
How would you figure out the members’ favourite activity? Give 1 reason for your answer.
___________________________________________________________________________
___________________________________________________________________________
Check Your Understanding
Communicate the Ideas
1.
Look at the cartoon. Explain how this sample could result in a false prediction.
_______________________________________________________________________________
_______________________________________________________________________________
11.3 Probability in Society ● MHR 643
Name: _____________________________________________________
2.
Date: ______________
You need to choose what flavours of ice cream to sell at a soccer tournament.
How could you use experimental probability and theoretical probability to help choose?
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
Practise
3.
A light bulb factory samples light bulbs as they come off the assembly line.
A random sample shows that 1 bulb out of every 20 does not work.
The manager predicts that 50 bulbs out of 1000 will not work.
a) How did the manager make his prediction?
1
×
20
1 ÷ 20 = ?
=
×
=
bulbs
b) What assumption did the manager make?
____________________________________________________________________________
____________________________________________________________________________
4.
A toothpick factory samples every 100th toothpick for damage.
The sample shows a 1% probability of damage.
How many toothpicks out of 2 million toothpicks do you predict will be damaged?
1
×
100
=
644
toothpicks
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
5.
Date: ______________
A movie rental company has 5 types of movies: drama, comedy, horror, action, and science fiction.
a) What is the theoretical probability that a person will choose a comedy?
P(comedy) = number of favourable outcomes
number of choices
b) What assumptions did you make?
____________________________________________________________________________
c) The table shows the movie preferences from a
random survey of 50 customers.
Predict the probability that a customer will
choose a comedy movie.
P(comedy) = number of favourable outcomes
number of responses
Movie Type
Responses
Drama
Comedy
Horror
Action
Science fiction
15
5
12
16
2
The probability that a customer will choose a comedy movie is
out of 50 or
%.
d) Give 1 reason why the theoretical probability is different from the experimental probability.
____________________________________________________________________________
____________________________________________________________________________
11.3 Probability in Society ● MHR 645
Name: _____________________________________________________
Date: ______________
Apply
6.
Jack wants to know the weekly part-time earnings of grade 9 students.
He randomly surveys 5 grade 9 students.
The results are: $75, $125, $25, $250, and $25.
a) Is this a biased sample? Circle YES or NO. Give 1 reason for your answer.
____________________________________________________________________________
b) Jack says that grade 9 students who work part-time earn an average of $100 per week.
Do you agree? Explain and show your thinking.
____________________________________________________________________________
7.
Miya received these scores from 10 judges in a skating competition. The scores are out of 10.
Judge
Score
1
8.5
2
6
3
6.5
4
6.5
5
6.5
a) Use all 10 judges’ scores to find Miya’s
mean score.
6
7
7
6
8
6.5
9
4.5
10
7
b) Use the first 3 judges’ scores as a sample.
Calculate the mean.
c) Use the last 3 judges’ scores as a sample. Calculate the mean.
d) Compare the mean from each sample to the mean for all judges.
Are the samples good predictors for Miya’s overall score? Circle YES or NO.
Give 1 reason for your answer.
____________________________________________________________________________
____________________________________________________________________________
646
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
Math Link
Use data from studies and surveys for your research project.
Use the library or the Internet.
a) Use your research question from Math Link 11.2 on page 634.
What data will you look for?
_______________________________________________________________________________
_______________________________________________________________________________
Where will you look?
_______________________________________________________________________________
_______________________________________________________________________________
b) Answer the following questions for 2 studies or surveys related to your question.
• Did the sampling method involve the whole population or a sample? Describe.
Study 1:
Study 2:
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
• How was the data collected? Describe.
Study 1:
Study 2:
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
11.3 Math Link ● MHR 647
Name: _____________________________________________________
Date: ______________
• What were the results for each method?
Study 1:
Study 2:
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
• What assumptions were made?
Study 1:
Study 2:
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
• How accurate are any predictions made about the population?
Study 1:
Study 2:
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
• Where did you find each study or survey? Who wrote each study?
648
Study 1:
Study 2:
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
11.4 Warm Up
1.
What is the difference between surveying a population and surveying a sample of a population?
A sample is a
2.
of a population.
Give an example or a description of each of the following:
a) biased sample
_____________________________________________________________________________
_____________________________________________________________________________
b) convenience sample
_____________________________________________________________________________
_____________________________________________________________________________
c) random sample
_____________________________________________________________________________
_____________________________________________________________________________
d) voluntary response sample
_____________________________________________________________________________
_____________________________________________________________________________
3.
a) How could the fisheries department estimate the average number of sea lice on salmon without
looking at every salmon caught?
The fisheries department could take a
lice on them.
of salmon and count the sea
They could then find the
number of sea lice and assume the
same is true for the whole
.
b) If there are 90 sea lice on 30 salmon, what is the average number of sea lice per salmon?
Sentence: _______________________________________________________________________
11.4 Warm Up ● MHR 649
Name: _____________________________________________________
Date: ______________
11.4 Developing and Implementing a
Project Plan
Step 1:
Finalize your research project.
1.
The animal you are studying is
2.
List 2 things you know about the animal:
.
________________________________________________________________________________
________________________________________________________________________________
3.
Write the population information you found in your research.
________________________________________________________________________________
________________________________________________________________________________
4.
Explain 1 possible reason why the animal is endangered.
________________________________________________________________________________
________________________________________________________________________________
5.
List where you got your information.
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
6.
Describe how the scientists collected the data.
How did they use the data to make a hypothesis about the health
of the animal population?
Literacy Link
A hypothesis is a statement that
guides an experiment.
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
650
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
Step 2:
Create a rubric for your research project.
The expectations are listed in column 1. For each expectation, write an explanation for each of the
4 levels of performance.
•
•
•
•
Level 1 is for work that does not meet the expectation.
Level 2 is for work that meets the minimum expectation.
Level 3 is for work that meets the expectation.
Level 4 is for work that is better than the expectation.
The first row is done for you.
Expectation
Planning
• question and
hypothesis
• description of
population
Level 1
Level 2
Level 3
Level 4
• not clear
• fairly clear
• mostly clear
• very clear
• limited or not
• some
• good enough
• detailed
complete
description
description
description
Performing
• research and
data collection
Recording
• display of
data
Analysing
• analysis
• conclusion(s)
Presenting
• project plan
and evaluation
of results
11.4 Developing and Implementing a Project Plan ● MHR 651
Name: _____________________________________________________
Date: ______________
Step 3:
Develop the project plan.
a) Describe how you will organize and display your data. Will you use a table?
What type of graph will you use?
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
b) Describe how you analysed the data from the studies.
• What assumptions did you make?
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
• If you made any predictions, how close were they?
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
c)
Describe how you will present your findings. Will you make a poster, do an oral or written
presentation, use technology, or use a combination of methods?
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
652
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
Step 4:
Complete the project.
a) Display the data on a graph.
b) Make a prediction from your data.
________________________________________________________________________________
________________________________________________________________________________
c)
Answer the following questions to evaluate your results.
• Do the data answer your question from Math Link 11.2? Circle YES or NO.
• Do you need to do more research? Circle YES or NO.
• Are the data biased? Circle YES or NO. Give 1 reason for your answer.
________________________________________________________________________________
• Write 2 questions you could ask as a result of your research.
________________________________________________________________________________
________________________________________________________________________________
• What other sampling methods could the researchers have used?
________________________________________________________________________________
________________________________________________________________________________
11.4 Developing and Implementing a Project Plan ● MHR 653
Name: _____________________________________________________
Date: ______________
Step 5:
Present your findings in a format of your choice. You must include
‰ a title
‰ a research question
‰ a description of the population
‰ for the studies researched,
– the sampling methods
– the data collection methods
– the results and conclusions
‰ your display of the data
‰ your answer to research question
‰ your evaluation of your research results
‰ a bibliography of all sources
Math Link: Wrap It Up!
Step 6:
a) Describe 1 good thing you learned from the research about your animal.
_______________________________________________________________________________
b) What is 1 thing that makes studying your animal’s whole population challenging?
_______________________________________________________________________________
c)
What 1 thing could be done to increase the probability of your animal’s survival?
_______________________________________________________________________________
d) Does your research suggest your animal will survive without the help of people?
How do you know?
_______________________________________________________________________________
e)
Write 1 sentence that describes what you have learned from your research.
_______________________________________________________________________________
f)
What should scientists do next to find out more about your animal’s survival?
_______________________________________________________________________________
g) What is the main type of sampling used to study your animal? What other methods could be used?
_______________________________________________________________________________
654
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
Graphic Organizer
Define each term and give an example.
Non-random
convenience:
Random
stratified:
voluntary:
systematic:
Sample
Data Analysis
Population
Influencing Factors
Examples:
Definition:
Example:
Graphic Organizer ● MHR 655
Name: _____________________________________________________
Date: ______________
Chapter 11 Review
Key Words
For #1 to #9, write the number that matches the description.
1. an example is every 10th person in a line-up
convenience sample
2. bias and cost are examples of these
population
3. an example is polling 2 students out of 100
about who will win an election
influencing factors
sample
4. an example is the first 30 people entering the
gates at a football game
5. any group of individuals selected from a
population
biased sample
voluntary response sample
random sample
6. a specific number of people selected from a
population
systematic sample
7. the whole group of people being studied
stratified sample
8. an example is dividing the population into
males and females and then randomly selecting
a proportional number from each group
9. an example is a population invited to call in to
a radio talk show
11.1 Factors Affecting Data Collection, pages 618–624
10. Name 1 influencing factor for each situation.
Influencing factors:
• bias
• use of language
• ethics
• cost
• time and timing
• privacy
• cultural sensitivity
a) Ask the first 40 people entering a park office if they think parks are worth the cost.
_____________________________________________________________________________
b) Ask 10 randomly chosen grade 8 students if the grade 12 students should have a special dance.
_____________________________________________________________________________
c) Ask 15 juice drinkers if they support replacing juice in the vending machine with bottled water.
_____________________________________________________________________________
656
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
11. Write 1 influencing factor that may affect data collection.
Then, rewrite the survey question.
a) You look like a good citizen. Do you support more money for hospitals?
Influencing factor:
Rewrite question: ______________________________________________________________
_____________________________________________________________________________
b) Everybody loves The Rockets. Who is your favourite rock group?
Influencing factor:
Rewrite question: ______________________________________________________________
_____________________________________________________________________________
c) Do you prefer ice hockey or cake after school?
Influencing factor:
Rewrite question: ______________________________________________________________
_____________________________________________________________________________
11.2 Collecting Data, pages 626–634
12. Identify the population for each situation. Then, describe how you would select a sample for each.
a) the spending habits of teens in Canada
Population:
I would select a sample by _______________________________________________________.
b) the popularity of different kinds of music in your school
Population:
I would select a sample by _______________________________________________________.
c) the cost of gasoline in your community
Population:
I would select a sample by _______________________________________________________.
Chapter 11 Review ● MHR 657
Name: _____________________________________________________
Date: ______________
13. For each situation, identify the type of sample. Identify any bias in each sample.
a) Survey the first 20 shoppers to enter the north entrance of a mall.
Sample type:
There could be bias because _____________________________________
Types of samples:
• convenience
• voluntary
• random
• stratified
• systematic
____________________________________________________________.
b) Divide youth conference delegates into groups according to the western province or territory
where they live. Then, randomly select 20 youths from each group.
Sample type:
There could be bias because _____________________________________________________.
c) The area supervisor for a fast-food chain selects employees at 1 store location.
Sample type:
There could be bias because _____________________________________________________.
____________________________________________________________________________
14. What type of sample do you suggest for each situation?
Give 1 reason for your choice.
a) a survey of customers to find out their favourite sundae topping
Type:
Reason: ______________________________________________________________________
_____________________________________________________________________________
b) a survey of doctors, nurses, and hospital administrators to find out if the hospital needs to add
more patient rooms
Type:
Reason: ______________________________________________________________________
_____________________________________________________________________________
658
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
11.3 Probability in Society, pages 636–648
15. A town of 4000 people is electing a mayor.
A reporter asked 40 people who they voted for.
He found that 50% chose Candidate A, 20% chose Candidate B, and the rest chose Candidate C.
a) How many people surveyed chose Candidate B?
Sentence: ____________________________________________________________________
b) What is the theoretical probability that a voter will choose Candidate A?
P (Candidate A) =
=
number of Candidate A’s
total number of candidates
1
What assumption did you make? __________________________________________________
Use the survey results.
c) Compare the experimental and theoretical probability of Candidate A winning.
_____________________________________________________________________________
d) The reporter predicts that Candidate A will win the election.
Do you agree with his prediction? Circle YES or NO. Give 1 reason for your answer.
_____________________________________________________________________________
16. Nancy is running for treasurer on student council.
There are 28 students in her class. Twenty classmates say they will vote for her.
Nancy predicts that 75% of the 328 grade 9 students will vote for her.
a) Is her prediction reasonable? Show your thinking.
Change
20
to a percent.
28
Sentence: ____________________________________________________________________
b) Write a prediction that would be more accurate.
____________________________________________________________________________
____________________________________________________________________________
Chapter 11 Review ● MHR 659
Name: _____________________________________________________
Date: ______________
Key Word Builder
Fill in the blanks with the correct key word. Then, find each word in the word search.
BIASED
CONVENIENCE
POPULATION
RANDOM
SAMPLE
STRATIFIED
SYSTEMATIC
VOLUNTARY
1.
A
of the population in a federal election might be 100 individuals
from each province or territory.
2.
A
whole population.
3.
A
sample means dividing the whole population into distinct groups,
then choosing the same percent of members from each group.
4.
A company interviews every 10th person on the payroll list. This is a
sample.
5.
The
6.
A sample is
7.
The research company invites all the residents of a town to participate in a survey.
sample means choosing a certain number of individuals from the
in a federal election is all eligible voters.
when it does not represent the whole population.
This is a
8.
response sample.
Rhett only surveyed students who were his friends because they were easy to access.
This is an example of a
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MHR ● Chapter 11: Data Analysis
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Date: ______________
Chapter 11 Practice Test
For #1 to #4, choose the best answer.
1.
A company displayed 2 sports shirts at a school with 500 students.
The students were asked the following question.
Over 78% of students at
Central High will buy Shirt B.
Which one of these two sports shirts would you buy?
A: $35.99
B: $44.99
What influencing factor might affect the data being collected?
2.
3.
4.
A bias
B timing
C ethics
D cultural sensitivity
Diana wants to survey grade 9 students about their favourite flavour of soft drink.
Which question is most appropriate?
A Is cola your favourite type of soft drink?
B Do you like soft drinks?
C What is your favourite flavour of soft drink?
D What brand of soft drink do you like?
An eco-tourism company is researching how to expand its tours.
It divides the western provinces into 8 areas.
Then, it surveys 10% of the population in each area. Which sampling method is this?
A convenience sample
B stratified sample
C systematic sample
D voluntary response sample
A business sends questionnaires to 50% of its employees randomly selected from a list.
Which sampling method is this?
A convenience sample
B stratified sample
C systematic sample
D voluntary response sample
Complete the statements in #5 to #7.
5.
A small group that represents a population is a
.
6.
Choosing members of the population at fixed intervals from a membership list describes a
.
7.
A Web site that asks browsers to fill out an online survey is using a
.
Chapter 11 Practice Test ● MHR 661
Name: _____________________________________________________
Date: ______________
Short Answer
8.
Cheyenne surveys students in her high school about types of music for a school dance.
They can choose rap, alternative, rock, or country.
a) What is the population for this study?
The population is
.
b) Write a clear survey question that is free from influencing factors.
_____________________________________________________________________________
_____________________________________________________________________________
c) Describe a sampling method Cheyenne could use.
_____________________________________________________________________________
_____________________________________________________________________________
9.
On an assembly line for cell phones, a random sample shows 3% are defective.
a) How many do you predict would be defective if 3248 were made?
Sentence: _____________________________________________________________________
b) Write 1 assumption you made in your prediction.
_____________________________________________________________________________
_____________________________________________________________________________
662
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
Date: ______________
Challenge
Global Warming
Tornados, floods, droughts, tsunamis, killer heat waves, and other extreme
weather events often make the news.
Many climate scientists link extreme weather events to global warming.
You be the climate scientist. Collect and analyse weather data to
determine if there is a warming trend in a location of your choice.
a) Use the Internet or the library to find
temperature information for your
location.
Find the mean annual temperatures for
each year for the last 10 years.
Location:
Year
Mean Annual
Temperature (°C)
b) Graph your data.
y
Mean Annual Temperature (ºC)
1.
x
Year
2.
a) Is there a warming trend in the area you analysed? Circle YES or NO.
Give 1 reason for your answer.
_____________________________________________________________________________
b) Do your findings support global warming? Circle YES or NO.
Give 1 reason for your answer.
_____________________________________________________________________________
Challenge ● MHR 663
Name: _____________________________________________________
Date: ______________
Chapters 8–11 Review
Chapter 8 Solving Linear Equations
1.
Solve each equation. Write your answers in lowest terms.
a) 8x =
2
5
8x ÷
b)
=
2
÷
5
x=
2
×
5
x
5
=
6
9
×
x
5
= ×
6
9
x=
2.
A triangle has an area of 10.54 m2 and a base length of 6.2 m.
What is the height of the triangle?
A= b×h
2
h
b = 6.2 m
Sentence: _______________________________________________________________________
3.
Bruno bought 4 boxes of granola. He received $6.04 in change from a $20.00 bill.
How much did he pay for each box of granola?
Let b = cost of 1 box of granola.
Cost of 4 boxes of granola + 6.04 = 20.00
Equation:
Solve:
Sentence: ________________________________________________________________________
664
MHR ● Chapter 11: Data Analysis
Name: _____________________________________________________
4.
Date: ______________
Two electricians each charge a fee for a service call, plus an hourly rate for their work.
Theo charges $49.95 plus $40.00 per hour.
Vita charges $69.95 plus $32.00 per hour.
For what length of service call do Theo and Vita charge the same amount?
Let x = the number of hours of service.
Theo
Vita
Initial Fee
Hourly Rate
Total Charge for Service
Theo’s total charge for service = Vita’s total charge for service
Sentence: ________________________________________________________________________
5.
The equilateral triangle and the square have equal perimeters.
What is the side length of the square?
Perimeter of triangle = perimeter of square
3x + 4
(
The value of x is
+
)=
(
+
2x + 5
)
.
Find the side length of the square.
2x + 5
Sentence: ________________________________________________________________________
Chapters 8–11 Review ● MHR 665
Name: _____________________________________________________
Date: ______________
Chapter 9 Linear Inequalities
6.
Write the inequalities using algebra.
a)
14
16
18
20
b)
-7
-6
-5
and
x
(≤ or ≥) (16 or 17 or 18)
7.
Show each inequality using a graph.
a) x < – 6
b) x ≥ 2.4
-10-9-8 -7 -6 -5 -4 -3 -2 -1 0 1
8.
1
2
3
Write an inequality to show each politician’s election promise.
a) We will start at least 8 new highway projects.
Variable: Let h = the number of highway projects.
Inequality: h
8
(≤ or ≥)
b) There will be a budget surplus of over $1.3 million this year.
Surplus means
extra money.
Variable: _____________________________________________________________________
Inequality:
9.
Solve each inequality.
a) x + 6.2 < 15
b) –25x < 125
When multiplying or dividing
by a negative number, reverse
the inequality symbol.
c)
666
x
≥ –10
5
MHR ● Chapter 11: Data Analysis
d) 20 – x ≤ 8
Name: _____________________________________________________
Date: ______________
10. Solve the inequality. Then, verify the solution.
4x + 17 ≥ 35
Check a value for equal:
Left Side
Subtract 17.
4x + 17
Right Side
35
Divide by 4.
Check a value for greater than:
11. Lori is renting a climbing wall.
The rental charge is $145/h.
She cannot spend more than $800.
For how many hours can Lori rent the wall and still stay within her budget?
a) Write an inequality to model this problem.
Variable: Let h = __________________________________________.
Inequality:
b) Solve the inequality and write a sentence to explain the situation.
Sentence: _____________________________________________________________________
Chapters 8–11 Review ● MHR 667
Name: _____________________________________________________
Date: ______________
Chapter 10 Circle Geometry
12. a) What is the measure of ∠DEB?
D
∠DEB is a(n)
angle.
∠DEB = ∠DAB because they share the same
So, ∠DEB =
.
C
A 47°
B
°.
E
b) What is the measure of ∠DCB? Justify your answer.
∠DCB is a
angle.
∠DCB =
×∠
=
×
=
°
So, ∠DCB is
°
°.
13. CD bisects chord AB.
radius = 7 cm
chord AB = 9 cm
What is the length of CE?
Round your answer to the nearest tenth.
cm
A
Label the diagram with the measurements you know.
Chord AB =
, so AE =
2
2
Formula → CE +
2
=
Substitute →
Solve →
The length of CE is
668
cm.
MHR ● Chapter 11: Data Analysis
C
cm
E
D
B
Name: _____________________________________________________
Date: ______________
E
14. Radius CG is perpendicular to chord EF.
Chord EF is 7 mm from C.
radius = 25 mm
What is the length of chord EF?
7 mm
C
Draw a line from C to F.
Write the measurements on the diagram.
H
G
F
Formula →
Substitute →
Solve →
FH is
mm.
EF = FH ×
=
Influencing factors:
● bias
● use of language
● ethics
● cost
● time and timing
● privacy
● cultural sensitivity
×
=
The length of chord EF is
mm.
Chapter 11 Data Analysis
15. For each survey question, write 1 influencing factor.
Then, rewrite the question to improve it.
a)
Do you like to play cards, the greatest
indoor game?
YES NO
b)
The student council wants to know how
cheap you are! Do you want a real band
($10 per ticket), or just a DJ ($5 per
ticket) at the dance?
Influencing factor:
Influencing factor:
Rewrite question:
Rewrite question:
Chapters 8–11 Review ● MHR 669
Name: _____________________________________________________
Date: ______________
16. You decide to survey students about their online activities.
a) What is the population?
b) List 2 different sampling methods you could use.
and
17. A recreation centre offers lessons in 5 types of activities: soccer, basketball, swimming, lacrosse,
and figure skating.
a) What is the theoretical probability that a person will choose swimming?
P(swimming) =
number of favourable outcomes
total number of outcomes
=
b) What assumptions did you make?
_____________________________________________________________________________
_____________________________________________________________________________
c) The table shows the activity preferences
from a random survey of 50 customers.
Predict the probability that a customer
will choose swimming.
P(swimming) =
number of favourable outcomes
total number of outcomes
Activity
Soccer
Basketball
Swimming
Lacrosse
Figure Skating
Number of Votes
15
5
12
16
2
=
=
← decimal
=
← percent
The probability that a customer will choose a swimming is
out of 50 or
%.
d) Give 1 reason why the theoretical probability is different from the experimental probability.
____________________________________________________________________________
____________________________________________________________________________
670
MHR ● Chapter 11: Data Analysis
Answers
Get Ready, pages 614–615
Apply
1. a) mean = 7; median = 6; modes = 8 and 15 b) mean = 4.5; median = 4.4;
no mode
6. Answers may vary. Examples: a) Which sport do you like best?
Participants: people between the ages of 13 and 19 b) What is most
important to your choice of cell phone: price or brand? Participants:
people about to purchase a cell phone c) Which Internet site do you
trust to give you accurate information? Participants: people who use
the Internet to find information.
2. a) 6 b) 24
3. a) A b) 17 L
Math Link
1.
7. Answers may vary. Examples: a) Do you drink juice? YES or NO.
If yes, would you switch to Crystal Juice? b) Do you use cough
medicines? YES or NO. If yes, which brands do you use? c) Do you
have Internet access? YES or NO. If yes, how satisfied are you with
the level of service you get?
Population
Approximate Total Park Count
(2007 Fall Count)
700
600
500
400
300
200
100
0
Math Link
Answers may vary. Examples:
Plains
Bison
Wood
Bison
Elk
Moose
Question #1: Do you think the Federal Government should create
National Parks? YES or NO.
Question #2: Does the cost of the land matter to you? YES or NO.
Question #3: Do you believe that people living on future National Parks
should be consulted? YES or NO.
Deer
Ungulate
Approximate Total Park Count
(2007 Fall Count)
11.2 Warm Up, page 625
1. Answers may vary. Examples: Since there are so many people who
live in a country, it might be difficult or expensive to survey all of
them.
Deer
Moose
2. more; more or less; less
3. a) 35 b) 197
Elk
4. a) 5% b) 20%
Wood bison
Plains bison
= 100 deer
= 100 moose
= 100 elk
= 100 wood bison
= 100 plains bison
5. 1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85, 92, 99
11.2 Collecting Data, pages 626–634
Working Example 1: Show You Know
2. Elk
3. a) 3 Elk b) 36%
11.1 Warm Up, page 617
1. a) approximately 98 books b) Adventure books
2. a) 66.7% b) NO. The circle graph shows 100% of the books they signed out.
3. 50
4. 10% of the school was surveyed.
11.1 Factors Affecting Data Collection, pages 618–624
Working Example 1: Show You Know
a) NO. Answers may vary. Examples: Asking only grade 12 students is not fair.
Asking only 10 students is not a large enough sample. b) The survey could be
improved by asking more students in a variety of grades.
Working Example 2: Show You Know
a) bias; Do you think the hunting of polar bears should be stopped? b) use of
language; Do you shop online? YES or NO. If yes, what kinds of products or
services do you buy?
Communicate the Ideas
1. Answers may vary. Example: Most students prefer rock and roll to jazz.
Would you prefer the school radio station to play more rock and roll or more
jazz?
2. a) bias b) time/timing c) cost
Practise
3. a) Ask hockey players if they are willing to pay higher registration fees for
hockey. b) Ask new motorcyclists if helmets should be mandatory.
c) Ask forestry workers if more money should be spent on fighting forest fires.
4. a) A survey asks how much parents earn in 1 year. b) Only teachers are
asked their opinion about a new school name. c) The Arts Council was
surveyed about the importance of art classes in schools.
5. Answers may vary. Examples: a) Do you like to watch hockey? b) What is
your favourite flavour of ice cream? c) Do you watch TV online? YES or
NO. If yes, what TV programs do you watch most online?
Answers may vary. Examples: a) the store’s customers; sample; it would
be difficult to get every customer to participate b) the restaurant’s
customers; sample; all customers might not want to participate
c) teachers in Canada who wear glasses or contacts; sample; it would be
too expensive and difficult to survey every teacher in the country.
Working Example 2: Show You Know
1. Answers may vary. Examples: a) voluntary response; use a suggestion
box in the library b) systematic; sample every 1000th person in phone
book.
2. a) random b) systematic c) voluntary response d) stratified
Communicate the Ideas
1. a) POPULATION b) NO; it is too expensive and difficult to survey
everyone.
2. a) SCOTT; the more people surveyed, the more accurate the response
will be. b) systematic sample; it would survey people who arrived late,
perhaps because they took their own vehicles rather than public transit.
3. Surveying the population means surveying every person in BC. A
sample is only a part of the whole population.
Practise
4. a) stratified b) convenience c) systematic d) random e) voluntary
5. a) teachers and students of the school; sample; it is less timeconsuming and expensive. b) customers who use the repair
department; sample; all customers might not want to be surveyed.
c) people with disabilities; sample; it would be difficult to find
everyone with a disability to survey.
Apply
Answers may vary. Examples:
6. a) population; there are not that many hospitals, so it is possible to
survey the population. b) sample; it would be hard to survey grade
9 students. c) population; all parachutes must be safe. d) sample; it
would be too expensive to test all tires.
7. Kristi could draw the names of 5 adults, 2 children, and 3 teens out of a
hat. This way, she would talk to 25% of each group.
Answers ● MHR 671
8. a) NO b) Erin’s friends are a specific group not a random selection.
9. a) Students who use the cafeteria. b) convenience c) YES. He is asking the
people who use the cafeteria.
2. It is one of the most endangered species in the world; there are only 25
living in the wild.
3. There were 300 in the mid-1980s, then 75 in 2001.
Math Link
4. Their habitat is disappearing.
Answers will vary. Examples: a) Vancouver Island marmot b) over 300; less than
75 in 2001 c) Clearcut logging affected their habitat. d) What can be done to
save the species? e) Random sampling was used because they had to catch the
marmots using traps. They could not control which ones they captured.
5. Internet sites and library books.
11.3 Warm Up, page 635
6. Scientists use systematic samples. Since they keep finding fewer and
fewer marmots, they know the population is in decline.
Step 2:
1. Answers may vary. Example: A weather forecast gives the probability of
precipitation. A high probability means it probably will rain or snow, but
doesn’t always mean it will for sure.
13
2
2. a)
; 0.25; 25% b) ; 0.4; 40%
52
5
3. a) mean = 10.6; median = 10; mode = 13 b) mean = 112.8; median = 111;
mode = 111 and 100
Expectation
Planning
11.3 Probability in Society, pages 636–648
Performing
Working Example 1: Show You Know
• research and
data
collection
Step 1: 21%
Step 2: 1512
Step 3: Approximately 1512 college students will have blue eyes.
Working Example 2: Show You Know
a) mean = 21.4; median = 22; no mode. Prediction: The average mark is
21.4
or 71.3%. b) YES; The last numbers contain more 20s, which is
30
common in the class, but not common in the first 5 numbers.
Apply
6. a) YES; the sample is too small. b) No; since the sample is biased, it could
be incorrect.
7. a) 6.5 b) 7 c) 6 d) Answers may vary. Example: YES; they are close to the
actual mean.
Math Link
a) Answers may vary. Example: I will look for experiments about the effect of
reintroducing marmots into the wild. I will look at the marmot research centre
online. b) Answers will vary.
11.4 Warm Up, page 649
1. part
2. Answers may vary. Examples: a) Asking only teachers about changing the
school hours. b) Asking only the people entering a mall about the
cleanliness of the mall. c) Picking names from a hat. d) Sending a
questionnaire in the mail.
3. a) sample; average; population b) The average number of sea lice on
90 salmon is 3.
11.4 Developing and Implementing a Project Plan, pages 650–654
Answers will vary. Examples:
Step 1:
1. The Vancouver Island marmot
• no research
or
incomplete
or
inappropriate
data
collection
• current
• excellent
• some
research
research
research
and data
and data
and current
collection
and
data from a
but may be sufficient to variety of
too little, or make
good
too old
conclusions sources
• data is in
• data is
• data is not • data is in
displayed;
table or
both table
displayed
can’t be
graph form and graph
clearly in a
understood only and is form and is variety of
fairly easy
easy to
easy-toto
understand understand
understand
formats
Recording
• display of
data
• analysis is • analysis
• unclear or • analysis
incorrect
can be
clear and
and
conclusions understood supports
conclusion
• conclusion(s)
and the
correct
are very
conclusion
conclusion clear and
makes some
entirely
sense
correct
Presenting
• project plan
and
evaluation of
results
• presentation
is unclear
or
incomplete
• presentation
is fairly
clear and
matches the
evaluation
of results
MHR ● Chapter 11: Data Analysis
• presentation
not only
explains the
project
results but
is highly
educational
as well
b) I assumed that no marmots had been bred in captivity. My prediction
was that there would be fewer left.
c) I will use a PowerPoint presentation to show pictures of the marmots,
their habitat, the effects of clear-cutting, and the graphs showing the
population change.
Step 4:
a)
Vancouver Island Marmot
Population
350
300
250
200
150
100
50
0
1980
1985
1990
1995
Year
672
• presentation
is clear and
matches the
information
found in the
project
Step 3:
a) My data will include a table that shows the populations each year and
a line graph that matches the data.
Population
4. 20 000
1
5. a)
b) That the chance of picking each type is equal. c) 5; 10%
5
d) Peoples’ preferences are not equally divided.
• very clear
• good
• some
• detailed
description enough
description
description
• analysis
3. a) 50 b) He assumed the sample was representative of the whole population.
Level 4
• description • limited or
of population not
complete
Analysing
Practise
Level 3
• fairly clear • mostly
clear
Communicate the Ideas
2. Experimental probability: Take a fair survey of soccer players to see their
favourites. Theoretical probability: If 4 flavours are offered, the theoretical
probability for each flavour is 25%.
Level 2
• question and • not clear
hypothesis
Working Example 3: Show You Know
a) Watching Movies: 50%; Bowling: 17.75% b) Answers may vary. Example:
I would add up the totals for each activity to find the most commonly picked
activity.
1. Answers may vary. Example: Taking too small a sample can result in a false
prediction because it doesn’t give fair or true results.
Level 1
2000
2005
b) I predict the population will continue to decline in the wild unless clearcutting is stopped.
c) Answers will vary.
16. Answers may vary. Example: a) Her prediction is not reasonable
because she only samples her class, which does not represent the
whole school. b) 70% of the grade 9 students will vote for Nancy.
Step 5: Answers will vary.
Key Word Builder, page 660
Math Link: Wrap It Up!, page 654
Answers will vary. Examples:
1. sample 2. random 3. stratified 4. systematic 5. population 6. biased
7. voluntary 8. convenience
Graphic Organizer, page 655
Answers will vary. Examples:
Convenience sample
Definition: choosing people who are easy to survey
Example: the students in my class
Voluntary response sample
Definition: people who are invited to take the survey
Example: an Internet site that asks readers to take a survey
Stratified sample
Definition: when the population is divided into groups and each group is fairly
surveyed
Example: 10 students are randomly surveyed from each grade in the school
Systematic sample
Definition: people on a list are fairly picked by their place on the list
Example: every 20th person in the telephone book is surveyed
Influencing factors
Definition: factors that affect the responses in a survey
Example: bias, language, ethics, cost, time and timing, privacy, cultural
sensitivity
Population
Definition: all the individuals in the group being studied
Example: the grade 12 population is all the students in grade 12
Chapter 11 Review, pages 656–659
1. systematic sample 2. influencing factors 3. biased sample
4. convenience sample 5. sample 6. random sample 7. population
8. stratified sample 9. voluntary response sample
10. a) time and timing b) bias c) bias
11. Answers may vary. Example: a) use of language; Do you support more
money for hospitals? Yes or No. b) bias; Do you listen to rock music? Yes
or No. If yes, who is your favourite rock group? c) use of language; If you
had to pick between the two, would you prefer to have snack after school or
to play a sport?
12. a) teens in Canada; randomly sampling high school students from across
Canada b) students at our school; randomly select 20 students from each
grade c) members of our community; systematically survey every 20th
person in community phone book
13. a) convenience; people entering from the north side might be from a
particular neighbourhood that doesn’t represent the mall population of
shoppers b) stratified; smaller provinces are over represented
c) convenience; the supervisor might only pick employees she likes
14. a) systematic sample; surveying every tenth customer would give a random
sample b) stratified sample; surveying 10% of doctors, nurses, and
administrators would be representative of the population
1
15. a) 8 people chose Candidate B. b) ; Each candidate has an equal chance
3
of being voted for. c) The experimental probability is greater than the
theoretical probability by about 17%. d) YES; The survey predicted
candidate A will receive the most votes by far.
S
T
N
G
R
E
E
F
E
Y
X
O
L
D
F
C
Y
Y
Q
X
E
A
M
C
Q
Q
Q
C
R
E
W
B
I
A
S
E
D
N
N
B
V
X
T
B
S
C
Y
D
H
M
E
R
G
E
C
N
M
Q
G
T
L
I
R
J
K
I
S
A
I
Y
J
Q
V
J
R
U
S
T
R
N
Y
X
E
N
P
W
O
R
V
A
R
A
K
A
L
N
V
W
E
D
L
N
Y
F
T
W
M
I
X
M
J
W
Q
V
U
O
Z
R
D
I
R
P
M
Z
C
E
F
D
N
G
K
M
V
V
F
Z
L
T
Z
I
B
T
T
O
H
C
Y
P
G
I
Y
E
L
Y
S
V
A
S
C
I
W
Y
Z
T
E
U
Z
R
G
H
R
T
X
Y
X
U
N
I
K
D
X
V
D
A
Y
T
L
X
Y
S
M
Q
V
U
I
N
O
I
T
A
L
U
P
O
P
N
M
A
L
Z
J
X
U
F
K
K
V
Z
K
J
V
F
Q
E
Y
Chapter 11 Practice Test, pages 661–662
1. A 2. C 3. B 4. D
5. sample
6. systematic sample
7. voluntary response sample
8. a) students in her high school b) Answers will vary. Example: Which
type of music would you most like played at the school dance? Choose
rap, alternative, rock, or country. c) Cheyenne could do a stratified
sample by selecting 20 students from each grade.
9. a) 97 cellphones would be defective. b) The sample represents the
population.
Challenge, page 663
Answers will vary. Example:
1. a) Data from Vancouver International Airport:
Year
Mean Annual Temperature (°C)
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
11.3
10.2
10.1
10.2
10.3
10.9
11.5
10.8
10.6
10.2
b)
Mean Annual Temperature (ºC)
11.6
11.4
11.2
Temperature
Step 6:
a) Marmots are being bred in zoos with the hope that they can be reintroduced
into the wild.
b) There are so few left they are difficult to find.
c) The government could protect marmot habitat so they have a place to live.
d) No. There are too few left to repopulate without human help.
e) The Vancouver Island marmot is almost extinct and needs a lot of help to
survive.
f) Scientists should find a way to reintroduce marmots into the wild.
g) The main type of sampling is systematic. Scientists could sample the whole
population.
11
10.8
10.6
10.4
10.2
10
1996 1998 2000 2002 2004 2006 2008
Year
2. a) No, there is not a warming trend because the temperatures ended up
lower than where they started. b) These findings do not support global
warming because the temperatures did not show any sort of trend.
Answers ● MHR 673
Chapters 8–11 Review, pages 664–670
1
15
1
1. a) x =
or 7
b) x =
20
2
2
10. x ≥ 4.5 or
9
1
or 4
2
2
2. The height is 3.4 m.
11. a) Variable: h = the number of hours; Inequality: 145h ≤ 800
b) h ≤ 5.5; Lori can rent the wall for 5.5 or fewer hours.
3. He paid $3.49 for each box.
12. a) 47° b) 94°
4. They charge the same amount for a 2.5 h service call.
13. 5.4
5. The side length of the square is 21 units.
3
6. a) x ≤ 17 b) x ≥ – 6 and x < –5
5
14. 48
7. a)
16. a) students b) Answers will vary. Example: convenience sample,
systematic sample
b)
-8
1
-7
-6
-5
2
3
8. a) ≥ b) Variable: Let s = budget surplus. Inequality: s > 1.3 million
9. a) x < 8.8 b) x > –5 c) x ≥ –50 d) x ≥ 12
674
MHR ● Chapter 11: Data Analysis
15. a) bias; Do you play cards? b) bias; Would you prefer a band or a DJ
at the dance?
1
b) Every activity has an equal chance of being
5
chosen. Customers have an equal interest in each activity. c) 12, 24%
d) Customers do not have an equal interest in each activity.
17. a) P(swimming) =