Chapter 01 - School District #35

CHAPTER
1
Representing Data
GET READY
2
Math Link
4
1.1 Warm Up
5
1.1 Advantages and Disadvantages of
Different Graphs
6
1.2 Warm Up
20
1.2 Misrepresenting Data
21
1.3 Warm Up
31
1.3 Critiquing Data Presentation
32
Chapter Review
40
Practice Test
44
Wrap It Up!
46
Key Word Builder
47
Math Games
48
Challenge in Real Life
49
Answers
50
Name: _____________________________________________________
Date: ______________
Bar Graphs and Double Bar Graphs
gy
Te
c
hn
olo
ry
sto
Hi
or
Fic
t
Sc
ien
Te
c
ce
Sp
gy
hn
ts
Zoe
Matt
ion
Number of Books
Zoe’s Books and Matt’s Books
14
12
10
8
6
4
2
0
olo
sto
ry
ts
Hi
or
Sp
Fic
t
ce
Sc
ien
double bar graph
● a graph that uses 2 sets of horizontal (↔) or
vertical (↕) bars to compare 2 sets of data
Zoe’s Books
14
12
10
8
6
4
2
0
ion
Number of Books
bar graph
● a graph that uses horizontal (↔)
or vertical (↕) bars to show data
This bar graph shows that Zoe
has twice as many science fiction
books as sports books.
This double bar graph shows that Matt has
twice as many sports books as Zoe has.
1. Look at the bar graph.
How many more science fiction books than history books does Zoe have?
–
=
2. Look at the double bar graph.
How many more science fiction books does Zoe have than Matt?
–
=
Circle Graphs
circle graph
● a graph that shows data using sections of a circle
● the sections in the circle graph must
add up to 100%
This circle graph shows the different activities that Akira
does online.
2
MHR ● Chapter 1: Representing Data
Akira’s Week on Internet (20 h)
Homework
12%
Surfing
13%
Watching
Videos
25%
Chat lines
50%
Name: _____________________________________________________
Date: ______________
3. Look at the circle graph.
How much more time does Akira spend on chat lines than surfing?
%–
%=
%
Line Graphs
line graph
a graph that uses a line to show
changes in data over time
Whitehorse Average Maximum
Temperature
This line graph shows changes in average
maximum temperature for each month in
Whitehorse, Yukon Territory.
trend
the general direction of a
line graph
Temperature (°C)
●
20
15
10
5
0
–5
–10
–15
●
J F M A M J J A S O N D
Month
To describe a graph’s trend, use words like: increasing, decreasing, rising, falling, etc.
4. Look at the line graph.
Describe the trend of the line graph.
Which month had the highest average maximum temperature?
_________________________________________________________________________
Pictographs
pictograph
● a graph that shows data using pictures and symbols
T-Shirts Sales
Monday
Tuesday
Wednesday
Thursday
Friday
This pictograph shows that more T-shirts were sold on
Thursday than on any other day.
represents 10 T-shirts
5. Look at the pictograph.
How many T-shirts were sold during the week?
+
+
+
+
=
Get Ready ● MHR 3
Name: _____________________________________________________
Date: ______________
Music Industry
Hundreds of millions of CDs are sold each year.
Music producers collect information to help them predict how
well a new CD will sell.
The circle graph shows the favourite types of music of
Canadians between the ages of 14 and 19.
a) What is the most popular type of music?
b) What is the least popular type of music?
c) The table shows the music market shares for different music producers.
market share
● a company’s percent of sales of a product in relation to the total sales
Draw a bar graph of the data.
ˆ Give the graph a title.
ˆ Label both axes.
ˆ Draw and colour the bars.
Music Producer
Sony BMG
Universal Music Group
Warner Music Group
EMI Group
Independent labels
35
30
25
20
15
10
5
0
4
Sony
BMG
Universal
Music
Group
Warner
Music
Group
EMI
Group
MHR ● Chapter 1: Representing Data
Independent
Labels
Market
Share (%)
26
32
15
9
18
Name: _____________________________________________________
Date: ______________
1.1 Warm Up
1. a) What type of graph is this?
Grade 8 Favourite Sports
b) What percent of students prefer volleyball?
Soccer
25%
c) How popular is hockey?
Basketball
Volleyball
20%
20%
Rugby
10%
Ro
3. Write each fraction in lowest terms.
Category
÷ _____
÷2
6
=
8
Shari’s Book Collection
Sc
Fic ien
tio ce
n
b) How many books does Shari have?
14
12
10
8
6
4
2
0
m Tee
an n
ce
Hi
sto
ry
Bi
og
ra
ph
y
Number of Books
2. a) What type of graph is this?
a)
Hockey
25%
4
b)
3
=
9
÷2
÷ _____
4. a) Count by 5s from 30 to 60.
_________________________________________________________________________
b) Count by 20s from 0 to 140.
_________________________________________________________________________
5. Write each number as a decimal.
a) 55% = 55 ÷ 100
b) 6%
=
6. Write each number as a percent.
a) 0.22 = 0.22 × 100
b) 0.03
=
1.1 Warm Up ● MHR 5
Name: _____________________________________________________
Date: ______________
1.1 Advantages and Disadvantages of Different Graphs
Working Example 1: Compare Two Graphs
interval
● the spread between the smallest and largest numbers in a range of numbers
The owners of Pascal’s Pizzeria keep track of the ways people order pizza.
They make a circle graph and a pictograph to show the data.
Weekend Pizza Sales (125 orders)
Weekend Pizza Sales
Walk In
32%
Phone
Phone
48%
Internet
Walk In
represents 10 pizzas
Internet
20%
a) How many more pizzas were ordered by phone than by Internet?
Solution
Look at the pictograph.
The symbol
represents
pizzas.
How many pizzas were ordered by phone? 10 ×
How many pizzas were ordered by Internet? 10 ×
=
=
How many more pizzas were ordered by phone than by Internet?
Telephone orders – Internet orders
=
–
=
more pizzas were ordered by phone than by Internet.
6
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
Date: ______________
b) Almost half of the orders were by phone.
Which graph shows this more clearly? Explain.
Solution
The circle graph shows that
% of the pizzas were ordered by phone.
The circle graph shows this more clearly because about
phone orders.
2
of the graph shows
c) Which graph should you use to show the number of pizzas ordered by Internet?
Explain your choice.
Solution
The pictograph is the best way to show the number of pizzas ordered by Internet.
It uses
to show
pizzas.
To show the orders by Internet, it uses
So, 2.5 × 10 =
pizza symbols.
pizzas are ordered by Internet.
The circle graph shows
% of the 125 pizzas were ordered by Internet.
To find the number of pizzas, calculate 20% of 125.
20% = 0.2
So, 0.2 × 125 =
pizzas.
d) Would a line graph work to show the data? Why or why not?
Solution
A line graph would not work because there is more than 1 category of pizza orders.
You need a graph that compares data in different categories.
e) What other kind of graph could you use to show the data?
Solution
You could also use a bar graph.
1.1 Advantages and Disadvantages of Different Graphs ● MHR 7
Name: _____________________________________________________
Date: ______________
The graphs show the number of each type of apple sold.
Type of Apples Sold
60
Number of Apples
Types of Apples Sold
Fuji
Golden Delicious
Jonagold
MacIntosh
50
40
30
20
10
Red Delicious
0
Fuji
represents 10 apples
Golden
Delicious
Jonagold MacIntosh
Red
Delicious
Type
a) In your opinion, which graph is easier to read? Give 1 reason for your choice.
_____________________________________________________________________
_____________________________________________________________________.
b) Could you show these data with a line graph? Circle YES or NO.
Give 1 reason for your answer.
_____________________________________________________________________
_____________________________________________________________________
c) What other type of graph could you use to display the data?
_____________________________________________________________________
d) How many more Fuji and MacIntosh apples were sold than Red Delicious apples?
Number of Fuji apples + number of MacIntosh apples
=
+
=
Total number of Fuji and MacIntosh  number of Red Delicious
=

=
8
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
Date: ______________
Working Example 2: Representing Data
During the 2005–2006 NHL season, the Edmonton Oilers played in the Stanley Cup finals.
Shawn Horcoff and Jarrett Stoll were 2 of the team’s top players.
Here are their statistics for the 3 seasons before 2005–2006.
Horcoff
Games
Played
78
80
79
Season
1
2
3
Goals
12
15
22
Stoll
Assists
21
25
51
Total
Points
33
40
73
Season
1
2
3
Games
Played
4
68
82
Goals
0
10
22
Assists
1
11
46
Total
Points
1
21
68
a) Make a double bar graph to show the data.
Solution
80
Total Points in 3 NHL Regular Seasons
70
Horcoff
60
Complete the graph by adding
the bars for Season 3.
Stoll
Points
50
40
30
20
10
0
1
2
3
Season
b) Which player improved the most in total points?
Solution
Stoll had
points in Season 1 and
–
Horcoff had
=
points in Season 1 and
–
points in Season 3.
points in Season 3.
=
improved the most in total points.
(Stoll or Horcoff)
1.1 Advantages and Disadvantages of Different Graphs ● MHR 9
Name: _____________________________________________________
Date: ______________
c) Coaches sometimes use total points to judge how good a player is.
Look at the number of games Horcoff and Stoll played.
Are total points a fair way to judge a player?
Horcoff
Season
1
2
3
Games
Played
78
80
79
Stoll
Goals
12
15
22
Assists
21
25
51
Total
Points
33
40
73
Season
1
2
3
Games
Played
24
68
82
Goals
20
10
22
Assists
21
11
46
Solution
How many games did Shawn Horcoff play in the 3 seasons?
Total games for Horcoff =
+
+
=
How many points did Horcoff score in total in the 3 seasons?
Total points for Horcoff =
+
+
=
How many games did Jarret Stoll play in the 3 seasons?
Total games for Stoll =
+
+
=
How many points did Stoll score in the 3 seasons?
Total points for Stoll =
+
+
=
Total points
a fair way to judge a player.
(are or are not)
Horcoff earned more total points than Stoll because he played more games than Stoll.
10
MHR ● Chapter 1: Representing Data
Total
Points
21
21
68
Name: _____________________________________________________
Date: ______________
d) Are the 2 circle graphs a good way to show these data? Why or why not?
Horcoff’s Total Points in 3
NHL Regular Seasons (146 points)
Stoll’s Total Points in 3
NHL Regular Seasons (90 points)
Season 1
1%
Season 1
22%
Season 3
49%
Season 3
76%
Season 2
23%
Season 2
29%
Solution
No, circle graphs are not a good way to show the data.
Each circle graph shows the
scored in each season,
(percent of points or number of games)
not the total number of points for each season.
It is
to see how many points each player scored in Season 2.
(easy or difficult)
Jenna surveyed 150 grade 8 students to find their favourite team sport.
Sports
Basketball
Volleyball
Soccer
Baseball
Hockey
Other
Frequency
24
20
45
25
32
4
ˆ Give the graph a title.
ˆ Label the x-axis. Mark the intervals.
ˆ Mark the intervals on the y-axis.
ˆ Draw bars for each sport.
Number of Students
a) Use a bar graph to show the data.
b) Explain 1 advantage of using a bar graph.
__________________________________
0
__________________________________
1.1 Advantages and Disadvantages of Different Graphs ● MHR 11
Name: _____________________________________________________
Date: ______________
1. Flora wants to use a graph to show ticket sales for 2 movies.
She is going to use the graph to predict future sales.
Movie Ticket Sales
5
4
Pirates
3
Top Speed
2
1
Ticket Sales ($ Millions)
Ticket Sales ($ Millions)
predict
● to make an educated guess about the future
0
Movie Ticket Sales
5
Pirates
4
Top Speed
3
2
1
0
1
2
3
4
5
6
1
Week
2
4
3
5
6
Week
Which graph should she use? Circle DOUBLE LINE GRAPH or BAR GRAPH.
Give 1 reason for your choice.
_________________________________________________________________________
2. Wes surveyed 60 students to find out which
type of computer game is most popular.
What type of graph should you use to display the data?
Circle BAR GRAPH or CIRCLE GRAPH.
Give 1 reason for your choice.
Type of Game
Quest
Role-play
Simulation
Strategy
Total
Votes
15
20
9
16
60
_______________________________________________
3. How are a bar graph and a pictograph alike?
____________________________________________________________________________
____________________________________________________________________________
4. How are a bar graph and a pictograph different?
____________________________________________________________________________
____________________________________________________________________________
12
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
Ravi’s Monthly
Spending ($200)
5. Ravi recorded how he spent his money for 1 month.
He spent $200 in total.
Savings
15% Movies
20%
Clothing
25%
Music
15%
Food
25%
Date: ______________
Ravi’s Monthly Spending
Movies
Music
Food
Clothing
Savings
represents $10
a) How much more money does Ravi spend on food than on movies?
1
represents $
Money spent on food = number of symbols × $10
=
×
=
Money spent on movies =
×
=
Food – movies =
–
=
Ravi spent
more on food than movies.
b) Which graph shows more clearly that Ravi spends more money on food than movies?
Give 1 reason for your answer.
_________________________________________________________________________
c) Ravi spends half his money on food and clothing. Which graph shows this more clearly?
Give 1 reason for your answer.
_________________________________________________________________________
d) What is 1 disadvantage of the pictograph?
_________________________________________________________________________
1.1 Advantages and Disadvantages of Different Graphs ● MHR 13
Name: _____________________________________________________
Date: ______________
6. Sara, Ann, and Min share 1 piano for their practice time.
The piano is available 40 h every week.
The graphs show how they share their practice time.
Piano Practice
Per Week (40 h)
Piano Practice
Per Week
Min
35%
Ann
40%
Students
Min
Sara
25%
Ann
Sara
0
5
10
15
20
Number of Hours
a) What information does each graph give?
Circle graph: ______________________________________________________________
Bar graph: ________________________________________________________________
b) Write 1 question about the data from the circle graph.
_________________________________________________________________________
_________________________________________________________________________
Answer your question:
_________________________________________________________________________
_________________________________________________________________________
c) Write 1 question about the data from the bar graph.
_________________________________________________________________________
_________________________________________________________________________
Answer your question:
_________________________________________________________________________
_________________________________________________________________________
14
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
7. For his science experiment, Mitchell measured
the height of a plant every Monday for 4 weeks.
He used a line graph and a pictograph to show his data.
Line graph: _______________________________
Plant Height
Plant Height
100
Height (cm)
a) What information does each graph give?
Date: ______________
Week 1
80
Week 2
60
Week 3
40
Week 4
20
represents 20 cm
0
_______________________________
1
2
3
4
Week
Pictograph: _______________________________
_______________________________
b) When did the plant grow the most?
Look at the line graph. Find the difference in height between weeks.
Week 4 – week 3
=
–
=
Week 3 – week 2
=
–
=
Week 2 – week 1
=
–
=
The plant height changed the most between week
and
.
c) How does the pictograph show the weeks that the plant grew at the same rate?
_________________________________________________________________________
d) What is 1 advantage of using a line graph?
_________________________________________________________________________
e) What is 1 advantage of using a pictograph?
_________________________________________________________________________
1.1 Advantages and Disadvantages of Different Graphs ● MHR 15
Name: _____________________________________________________
Date: ______________
8. The table shows the decibel levels of different sounds in the environment.
Sound
Leaves rustling
Whisper
Heavy traffic
Lawn mower
Hockey game
Thunder clap
Stock car race
Balloon pop
Level
20 dB
30 dB
78 dB
90 dB
104 dB
120 dB
130 dB
157 dB
Decibels measure the
intensity of sound.
a) Use a bar graph to show the
data in the table.
160
140
120
Level
ˆ Mark the intervals on the
x-axis.
ˆ Write the categories for
“Sound” under the x-axis.
ˆ Draw bars for each sound.
Decibel Levels
180
100
80
60
40
20
0
Sound
b) Give 1 reason why you might use a bar graph for these data.
_________________________________________________________________________
_________________________________________________________________________
c) Could you use a line graph to show the data? Circle YES or NO.
Give 1 reason for your answer.
_________________________________________________________________________
d) Could you use a pictograph to show the data? Circle YES or NO.
Give 1 reason for your answer.
_________________________________________________________________________
16
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
9. The pictograph shows the results of the student council election
for the grade 8 members.
Date: ______________
Grade 8 Member
Ari
Bai
a) Look at the pictograph.
How many votes does each symbol (
Niki
) show?
Tuong
represents 10 votes
b) Draw a bar graph to show the results in
the pictograph.
80
70
Number of Votes
ˆ Give the graph a title.
ˆ Mark the intervals on the x-axis.
ˆ Write the categories for “Grade 8 Member”
under the x-axis.
ˆ Draw a bar for each student.
90
60
50
40
30
20
10
0
Grade 8 Member
10. Janice surveyed 10 friends about their favourite colour of Freezie™.
She used a line graph to show the data.
Favourite Freezie™
Orange
Colours
Red
Blue
Pink
Purple
White
1
2
3
4
5
6
7
8
9
10
Votes
a) Why is a line graph not a good choice to show the data?
_________________________________________________________________________
b) What type of graph would be a better choice to show these data?
_________________________________________________________________________
1.1 Advantages and Disadvantages of Different Graphs ● MHR 17
Name: _____________________________________________________
Date: ______________
11. A radio station wants teens to use its Web site.
The radio station surveyed 50 students from 2 schools to find out what features would interest
students.
The students voted for the 2 features they most wanted to see on the site.
School
Queen
Elizabeth
Hillside
Entertainment
News
Music
Downloads
Contests
Message
Boards
40
45
5
10
20
35
25
20
a) What type of graph could you use to display the data?
b) Why did you choose this kind of graph?
_________________________________________________________________________
c) Which 2 categories are the most important for students from Queen Elizabeth School?
_________________________________________________________________________
d) Are these same categories most important for students from Hillside School?
_________________________________________________________________________
e) Graph the data in the table.
18
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
Date: ______________
Survey the students in your class about their favourite type of music.
Use the frequency table to record the data.
1. a) Write the names of 5 types of music in column 1 of the chart.
b) Ask each student in your class what his/her favourite type
of music is.
c) In column 2, use tally marks to record the number of times
students choose each type of music.
d) In column 3, total the number of tally marks.
Type of Music
Tally
Frequency
A frequency table
uses tally marks
to record the
number of times
each item occurs.
None of the above
2. Draw a bar graph of your data.
ˆ Give the graph a title.
ˆ Label the x-axis “Type of Music.”
Mark the intervals and
the names of each type of music.
ˆ Label the y-axis
“Number of Votes.”
Mark the intervals.
ˆ Draw bars for each
type of music.
3. What is 1 advantage of using a bar graph to show your data?
____________________________________________________________________________
4. What is 1 disadvantage of using a bar graph to show your data?
____________________________________________________________________________
1.1 Math Link ● MHR 19
Name: _____________________________________________________
Date: ______________
1.2 Warm Up
Favourite Type of Video Game
(200 students)
Other
8%
1. a) What information does the circle graph show?
Strategy
17%
________________________________________
Simulation
33%
Role Play
17%
b) What information does the bar graph show?
Trivia Quest
12% 13%
________________________________________
Ot
he
r
gy
te
St
ra
Pla
y
ia
le
t
Ro
Tri
v
es
n
Sim
ula
tio
d) Which graph shows more clearly the number of
people who enjoy role-playing games?
70
60
50
40
30
20
10
0
Qu
of people in each category?
Number of Students
Favourite Type of Video Game
c) Which graph shows the exact number
Type of Video Game
Give 1 reason for your answer.
_________________________________________________________________________
2. Would a line graph be a good way to show the data for #1? Give 1 reason for your answer.
____________________________________________________________________________
3. What other type of graph could you use to display the data?
4. You want to show 25% on a circle graph.
What fraction of the circle should you colour?
÷ 25
25% =
100
100
=
÷ 25
Sentence: ____________________________________________________________________
20
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
Date: ______________
1.2 Misrepresenting Data
Working Example 1: Distorting the Scale
distort
● to change the appearance or meaning of something in a way that is misleading
misleading
● to show data in a way that is confusing or is not accurate
The bar graph shows Matthew’s math test scores.
Matthew’s Test Scores
70
68
Score
66
64
62
60
0
Test 1
Test 2
Test 3
Test 4
Test
a) According to the graph, what score did Matthew get on each test?
Solution
He scored 60, 65,
, and
.
b) From the graph, what seems to be true about Matthew’s improvement on the last 4 tests?
Solution
The graph makes it look like Matthew has improved
.
(a lot or a little)
However, the data show this is not true.
The break in the scale on the y-axis is misleading.
A break in the y-axis of a graph means the length of the axis has been shortened.
The break can be shown as
or
1.2 Misrepresenting Data ● MHR 21
Name: _____________________________________________________
Date: ______________
c) How could you make the graph less misleading?
Solution
Draw the graph with a scale that starts at 0 and has no break.
Complete the graph for Test 4.
Matthew’s Test Scores
70
Matthew scored
on Test 4.
60
Score
50
40
30
20
10
0
Test 1
Test 2
Test 3
Test 4
Test
d) Look at the graph in part c). Describe Matthew’s test improvement.
Solution
Matthew’s test scores have improved a
amount over the last 4 tests.
The greatest increase is between Test
and Test
a) Explain how this graph could be misleading.
Price Per L ($)
(small or large)
_____________________________________
.
Gas Prices on Monday
1.19
1.14
0
7 a.m.
_____________________________________
7 p.m.
Time of Day
_____________________________________
b) Using the graph, what was the price of gas at the beginning of the day?
c) What was the price at the end of the day?
d) How would you redraw the graph to make it less misleading?
________________________________________________________________________
22
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
Date: ______________
Working Example 2: Distorting the Visuals
a) Look at the pictograph.
Which pet seems to be the favourite? Explain.
Favourite Pets of Grade 8 Students
Cat
Dog
Solution
Fish
represents the choice of 10 students
represents the choice of 10 students
seems to be the favourite
because the symbol is biggest.
represents the choice of 10 students
b) Does it seem that more students like cats or dogs?
Solution
It seems that more people like
than
because the line for dogs is
than the line for cats.
(longer or shorter)
c) How could you redraw the pictograph to show the data more accurately?
accurate
● to show data fairly, without errors
Solution
The symbols for each pet should be the
size.
(same or different)
The symbols should be the
distance apart.
(same or different)
Favourite Lunch Specials
a) Explain how this graph could be misleading.
_____________________________________
Pizza
Macaroni
and Cheese
Hamburger
represents the choice of 10 people
_____________________________________
represents the choice of 10 people
represents the choice of 10 people
b) What does the graph suggest about favourite lunch specials?
________________________________________________________________________
c) How could you redraw the graph to make it more accurate?
________________________________________________________________________
1.2 Misrepresenting Data ● MHR 23
Name: _____________________________________________________
Date: ______________
Working Example 3: Distorting the Size of Bars
5000
Computer Sales
4000
Number
Number
4000
3000
2000
1000
0
Computer Sales
5000
3000
2000
1000
Desktops
0
Laptops
Desktops
Category
Laptops
Category
Graph A
Graph B
a) Look at Graph A. How many more desktop computers were sold than laptops?
Does Graph A show the data accurately? Explain.
Solution
Graph A shows sales of 4000 desktops and
laptops.
The sales of desktops are
as high as the sales of laptops.
(twice or 3 times)
The bar for desktops is
as high as the bar for laptops.
(twice or 3 times)
The graph is accurate.
b) Look at Graph B.
Has the number of computers changed?
What is misleading about Graph B?
Solution
Graph B shows sales of 4000 desktops and
The number of computers sold
laptops.
changed.
(has or has not)
The bar for desktops is twice as wide as the bar for
.
The graph makes it look like the difference between the number of desktops and laptops
sold is greater than it actually is.
24
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
a) Explain how this graph could be misleading.
Annual Cost of Taking
Care of a Bike
_____________________________________________
40
Cost ($)
_____________________________________________
Date: ______________
20
0
b) What does the graph suggest about the cost in
2007 compared to the cost in 1997?
1997
2007
Year
____________________________________________________________________________________________
____________________________________________________________________________________________
c) How could you redraw this graph to make it more accurate?
____________________________________________________________________________________________
____________________________________________________________________________________________
1. Sophie surveyed her friends about their favourite flavour of ice cream.
Favourite Ice Cream
a) What information is missing on the graph?
Vanilla
20%
__________________________________
__________________________________
Strawberry
20%
Chocolate
60%
b) Write 2 ways Sophie could make her graph more accurate.
and
2. When would it help someone to make a misleading graph?
Give 1 example.
A misleading graph does
not show the data fairly.
____________________________________________________________________________
____________________________________________________________________________
1.2 Misrepresenting Data ● MHR 25
Name: _____________________________________________________
Date: ______________
3. The bar graph shows the election results for student council president.
Election Results
200
a) How many times taller does the bar for candidate B seem
Number of Votes
175
than the bar for A?
b) How many more votes did candidate B get than candidate A?
150
125
100
75
0
Votes for candidate B − votes for candidate A
A
B
C
Candidate
=
−
=
c) What does the graph seem to show about the election results?
_________________________________________________________________________
d) What is wrong with the scale on this graph?
_________________________________________________________________________
4. The graph in this advertisement shows the results of a taste test.
Move over Bonzo, The Big Cheese is in town!
a) Which hamburger seems to be the favourite?
Give 1 reason for your choice.
_________________________________________
The Big Cheese
56%
Bonzo Burger
44%
_________________________________________
b) Why does 1 hamburger seem to be more popular than the other?
_________________________________________________________________________
c) How can you make this graph more accurate?
_________________________________________________________________________
26
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
5. a) Which fruit seems to sell the best?
Give 1 reason for your answer.
__________________________________
Date: ______________
Fruit Sales in One Week
Apples
Peaches
Cherries
represents 20 kg
__________________________________
represents 20 kg
represents 20 kg
b) Who would want to make the graph this way?
Circle CHERRY GROWER or APPLE GROWER.
6. The graph shows how many video game levels that 2 friends have reached.
Quest Progress
a) How many levels ahead is Scott?
Players
Scott
b) Estimate how much bigger Scott’s bar is than Bryce’s bar.
Bryce
0
c) Write 2 misleading things about this graph.
10
12
14
16
18
Level Completed
and
600
Profit ($)
7. a) What does the graph show about the profits from
January to June?
_______________________________________________
b) Explain how this graph is misleading.
Profits
500
400
300
200
0
Jan Feb Mar Apr May June
_______________________________________________
Month
c) Redraw the graph on the grid.
ˆ Give the graph a title.
ˆ Label the x-axis “Months.”
Mark the categories.
ˆ Label the y-axis “Profits ($).”
ˆ Mark the intervals on the y-axis
from 0 to 600 with no break in the scale.
ˆ Plot the points for each month. Connect them.
d) What does your new graph show you about
the profits from January to June?
_________________________________________________________________________
1.2 Misrepresenting Data ● MHR 27
Name: _____________________________________________________
Date: ______________
8. Charles kept a record of his Math quiz scores for this term.
Quiz
Score (%)
1
65
2
69
3
75
4
72
5
77
6
80
a) Draw a bar graph that accurately shows his scores.
ˆ Give the graph a title.
ˆ Label the x-axis “Quiz Number.”
Mark the categories.
ˆ Label the y-axis “Score (%).”
ˆ Mark the intervals on the y-axis
from 0 to 80 with no break in the scale.
ˆ Draw bars for each score.
b) Draw a misleading bar graph that makes it look like Charles’ test scores are improving a lot.
ˆ Give the graph a title.
ˆ Label the x-axis “Quiz Number.”
ˆ Label the y-axis “Score (%).”
ˆ Mark the intervals on the y-axis
from 60 to 80, with a break in the scale
from 0 to 60.
ˆ Draw bars for each score.
c) How does your graph from part b) make it look like
Charles’ test scores are improving a lot?
_________________________________________________________________________
28
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
9. a) Which category does the government want
people to notice the most?
Date: ______________
Provincial Budget 2008–2009
Housing
13%
Energy
24%
Education
24%
b) Redraw the graph to make it more accurate.
Others
4%
Health
27%
Transportation
8%
Search the Internet, magazines, or newspapers for data
about the music sales of a musician or band.
Examples: total CD sales,
number of music downloads,
number of times played on
the radio, etc.
a) Who did you research?
b) Write 1 question you will research about music sales.
_________________________________________________________________________
c) Record the data you collected.
Use at least 2 sources. Write the source of your data.
Source
(Internet, magazine, newspaper, …)
Information
(data)
d) Write a statement about music sales based on the data you collected.
_________________________________________________________________________
1.2 Math Link ● MHR 29
Name: _____________________________________________________
Date: ______________
e) Draw a bar or line graph that supports your statement.
f ) Write a statement that is the opposite of what your graph shows.
_________________________________________________________________________
g) How could you change the graph to support your statement in part f )? Redraw the graph.
_________________________________________________________________________
30
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
Date: ______________
1.3 Warm Up
1. a) According to the graph, how many students prefer each city?
Québec City
8
7
Frequency
Charlottetown
School Trip Option
6
5
4
Toronto
3
0
b) Look at the graph. How many students voted?
wn
ity
to
te
lot
ar
Ch
e
éb
cC
Qu
to
on
r
To
Cities
c) How does the graph make Québec City seem much more popular?
_________________________________________________________________________
d) Out of the total number of students, how many voted for Québec City?
e) Did more than half of the whole group choose Québec City? Circle YES or NO.
f ) What other kind of graph could you use to show how many students chose each trip?
_________________________________________________________________________
2. Alan wants to use these symbols to draw a pictograph to show
if 10 people prefer soccer or basketball.
How could you make Alan’s symbols better?
__________________________________________________
3. a) In most cases, what number should the vertical axis (↕) of a graph start with?
b) Explain your answer.
_________________________________________________________________________
1.3 Warm Up ● MHR 31
Name: _____________________________________________________
Date: ______________
1.3 Critiquing Data Presentation
critique
● to judge or to make suggestions for improvement
Working Example: Critiquing a Graph
Two grade 8 classes wrote the same test. Bindi recorded all the students’ marks.
Class A (32 students)
Score (%)
50–59
60–69
70–79
80–89
90–99
Frequency
3
5
13
7
4
Class B (27 students)
Score (%) Frequency
50–59
2
60–69
3
70–79
8
80–89
13
90–99
1
She uses 2 circle graphs to show the data.
Class A Test Scores (32 students)
50-59%
9%
90-99%
13%
80-89%
22%
Class B Test Scores (27 students)
90-99%
4%
50-59%
7%
60-69%
11%
60-69%
16%
70-79%
40%
80-89%
48%
70-79%
30%
a) Why do you think Bindi used 2 circle graphs instead of 1?
Solution
There are more students in Class
than in Class
.
Bindi’s circle graphs compare percents and not the number of students in each category.
a group of data
32
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
Date: ______________
b) Are the graphs misleading? Explain.
Solution
No. The circle graphs give a true picture of the data.
Each circle is labelled with the percent of students in each category.
The title also tells how many students are in each class.
c) State 2 conclusions you can make based on Bindi’s circle graphs.
Solution
Most of the students in both classes scored between
More students in Class
% and 89%.
scored over 80% than in Class
.
d) Draw a double bar graph to show the same information Bindi used to make her circle
graphs.
Solution
Draw the bars for 80–89% and 90–99%.
Class A and Class B Test Scores
Number of Students
14
12
Class A
10
Class B
8
Use the table in part a).
6
4
2
0
50-59%
60-69%
70-79%
80-89%
90-99%
Score
e) List 1 advantage and 1 disadvantage of using a double bar graph to show the data.
Solution
A double bar graph lets you compare the
of students who
(number or percent)
scored in each interval.
Comparing the number of students in each interval is
(less or more)
meaningful because the class sizes are different.
1.3 Critiquing Data Presentation ● MHR
33
Name: _____________________________________________________
Date: ______________
A group of teens picked pears at an orchard.
The chart shows how many baskets each teen picked.
Number of
Baskets Picked
3
4
5
6
7
Tally
Frequency
|||
||||
|||| ||||
||||
3
5
9
5
3
|||
a) How many teens picked 4 baskets of pears?
b) What is the lowest frequency in the chart?
The circle graph shows the percent of teens that picked each number of baskets.
Baskets of Pears Picked (25 teens)
7
12%
3
12%
6
20%
4
20%
5
36%
c) What percent of teens picked 5 baskets?
d) What is an advantage of using the circle graph?
________________________________________________________________________
________________________________________________________________________
e) What conclusion can you make from the circle graph?
________________________________________________________________________
________________________________________________________________________
34
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
1. a) Look at the pictograph. Is this a good way to show the data
about how students get to school? Circle YES or NO.
Give 1 reason for your answer.
Date: ______________
Transportation
Walk
Bike
Drive
______________________________________________
represents 10 students
represents 10 students
represents 10 students
b) Is this pictograph misleading? Explain.
_________________________________________________________________________
c) Would changing the number of students each symbol represents make the graph better?
Circle YES or NO.
Give 1 reason for your answer. ________________________________________________
d) What other kinds of graphs could you use to show these data?
_________________________________________________________________________
2. Danny made this graph to record his running times over 6 weeks.
a) What is happening to Danny’s running times from
week 1 to week 6?
Running Times
90
88
________________________________________
86
Time (s)
________________________________________
84
82
80
78
b) How does the scale affect the way this
graph shows his running times?
76
0
1
2
3
4
5
6
Week
________________________________________
c) How would you improve this graph?
_________________________________________________________________________
3. Your friend missed the classes on how to critique graphs.
Explain how to judge a graph and why it is important to do so.
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
1.3 Critiquing Data Presentation ● MHR 35
Name: _____________________________________________________
Date: ______________
4. Madison surveyed grade 8 students about how they like to communicate with friends.
She made a graph of her results.
a) Why did Madison choose a double bar graph to
display her data?
Communicating With Friends
E-mail
_________________________________________
_________________________________________
b) Is this graph misleading?
Give 1 reason for your answer.
_________________________________________
_________________________________________
c) What is 1 conclusion you can make from the graph?
_________________________________________
Ways to Communicate
Text Messaging
Girls
Boys
Cell Phone
Telephone
In Person
Internet
0
2
4
6
8
10
12
14
Number of Students
_________________________________________
d) Madison made a double line graph to show the data.
Communicating With
Friends
Number of Students
14
12
10
8
6
Girls
Boys
4
2
In
In
te
rn
et
Pe
rso
Te
lep n
h
Ce one
Te ll P
xt
h
M one
es
sa
gin
g
Em
ail
0
Ways to Communicate
How is this graph misleading?
_________________________________________________________________________
_________________________________________________________________________
36
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
Date: ______________
5. a) Write 1 conclusion you can make from the graph.
_______________________________________
b) What is 1 advantage of using a double bar graph
to show these data?
Number of Students
_______________________________________
Time Spent on Internet
25
20
Grade 8
15
Grade 9
10
5
0
Less than 1 to less
1h
than 2 h
2 to less
than 3 h
3 to less
than 4 h
4 to less More than
than 5 h
5h
Time Per Week
_______________________________________
c) What other type of graph could you use to show
these data? Give 1 reason for your answer.
________________________________________________________________________
________________________________________________________________________
6. a) What is 1 conclusion you can make from this circle graph?
______________________________________________
Cars in Parking Lot (50 cars)
Other
8%
SUV
28%
______________________________________________
Sedan
36%
b) What is 1 advantage of using a circle graph instead
of another type of graph?
Minivan
20%
Compact
8%
______________________________________________
______________________________________________
Look at the title.
c) How many cars are in the parking lot?
d) What percent are compact cars?
e) Since 8% means 8 out of 100, how many cars is this out of 50?
÷ ______
8
=
100
50
÷ ______
This is
cars out of 50.
1.3 Critiquing Data Presentation ● MHR
37
Name: _____________________________________________________
Date: ______________
7. A ski rental company recorded the type of snowboards that were rented for 1 week.
A total of 287 snowboards were rented.
Snowboard Type Number
Freestyle
59
Freerider
138
Freecarve
49
Alpine
41
a) Draw a bar graph to show the data.
b) Write 1 conclusion you can make
based on your graph.
_____________________________
_____________________________
c) Write 1 advantage of using a bar graph.
_____________________________
_____________________________
8. Chloe surveyed grade 8 students about which charity group they would donate money to.
All 85 students in grade 8 voted once.
Chloe made 2 graphs to show the data.
Favourite Charity (85 votes)
International
Aid 20%
Health
38%
Favourite Charity
36
Number of Students
Environment
7%
Arts, Culture,
Sports 15%
30
24
18
12
6
W
ild
life
Int
ern
ati
on
al
Ar
Ai
ts,
d
Cu
ltu
re,
Sp
or
ts
En
vir
on
me
nt
Wildlife
20%
He
alt
h
0
Charity
a) Which charity group was the most popular? _____________________________________
b) Which graph shows exactly how many people voted for each charity? __________________
c) You want to convince the students to donate to a health charity.
Which graph would you use? Circle CIRCLE GRAPH or BAR GRAPH.
Give 1 reason for your answer.
_________________________________________________________________________
_________________________________________________________________________
38
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
a) Why does it look like blue calculators are about
3 times more popular than orange calculators?
Calculators Sold by Colour
60
50
Number
9. Truong recorded the sales of calculators at a dollar store.
He wants to know what colour people like best.
Truong drew a bar graph to show his data.
Date: ______________
40
30
20
0
Pink
Blue
________________________________________
Orange
Silver
Black
Colour
b) What could you do to make this graph more accurate?
_________________________________________________________________________
c) What other kind of graph could Troung use to display his results?
Give 1 reason for your answer.
_________________________________________________________________________
Organizers for a music concert are deciding between 2 performers.
They want to use data from record sales to help make their decision. Look at the graphs.
Recording Sales Over 6 Months
Recording Sales Over 6 Months
35
A
A
43%
B
57%
Sales (1000s)
30
B
25
20
15
10
5
0
J
F
M
A
M
J
Month
a) What information does the circle graph show?
_________________________________________________________________________
b) What information does the bar graph show?
_________________________________________________________________________
c) The organizers want a large crowd to come to the concert.
Which performer should they choose? Give 1 reason for your answer.
_________________________________________________________________________
1.3 Math Link ● MHR 39
Name: _____________________________________________________
Date: ______________
1 Chapter Review
Key Words
For #1 to #5, write the number that matches the description.
1. compares categories using percents
bar graph
2. compares 1 kind of data using bars
double bar graph
3. uses symbols to show data in units
line graph
4. shows changes in data over time
circle graph
5. compares 2 sets of data in different categories
pictograph
6. The graphs both show the number of books
in a classroom library.
a) Which graph helps you find how many more
sports books there are than history books?
Classroom Library
Books (48 books)
Fiction
50%
Science
Fiction
25%
Sports
19%
Number of Books
1.1 Advantages and Disadvantages of Different Graphs, pages 6–19
25
20
15
10
5
0
Classroom Library
Books
Science Sports History Fiction
Fiction
Category
History
6%
b) Which graph helps you decide how to spend $1000 on new books for the library?
Give 1 reason for your answer.
_________________________________________________________________________
c) How much money should be spent on each type of book? Show your work.
Fiction = 50% of $1000
= 0.50 × 1000
50% = 50 ÷ 100
= 0.50
Science fiction =
= 0.
=$
=$
Sports
40
MHR ● Chapter 1: Representing Data
History
% × 1000
× 1000
Name: _____________________________________________________
Date: ______________
7. Describe a situation where you would use each type of graph.
a) Bar graph _________________________________________________________________
b) Circle graph _______________________________________________________________
c) Double bar graph ___________________________________________________________
d) Line graph ________________________________________________________________
1.2 Misrepresenting Data, pages 21–30
8. The graph shows the number of electronic devices that grade 8 students own.
Electronic Devices Owned
by Grade 8 Students
Device
Computer
Cell Phone
MP3 Player
0
26
28
30
32
34
36
38
40
42
Number
a) The graph shows that students own more computers than MP3 players and cell phones
together. Is this true? Circle YES or NO.
b) How do you know?
Number of MP3 players + number of cell phones
=
+
Number of computers
=
=
_________________________________________________________________________
c) How could you change the graph to make it more accurate?
_________________________________________________________________________
_________________________________________________________________________
Chapter Review ● MHR 41
Name: _____________________________________________________
9. A company makes 2500 school lockers each day.
Lockers are rejected if they are not made well.
The table shows how many lockers were rejected during 1 week.
a) On which day were the most lockers rejected?
b) On which day were the least lockers rejected?
c) What is the difference between the day with the
most rejections and the day with the least rejections?
Date: ______________
Number
Day
Rejected
Monday
45
Tuesday
40
Wednesday
25
Thursday
30
Friday
35
Total
175
Difference means subtract.
d) Draw a misleading pictograph to exaggerate the number of lockers rejected on Monday.
ˆ Give the pictograph a title.
ˆ List the days on the left side.
ˆ Draw your symbol (picture) at the bottom of the graph.
Show how much each picture represents.
ˆ Draw pictures to represent the number of lockers rejected each day.
42
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
Date: ______________
1.3 Critiquing Data Presentation, pages 32–39
10. The circle graph shows what percent of the students are right-handed,
left-handed, or ambidextrous.
someone who can use
both hands equally well
Right-Handed, Left-Handed,
or Ambidextrous?
(58 students)
Left-Handed Ambidextrous
9%
11%
a) Write 2 things you can conclude from the graph.
●
____________________________________________________
●
____________________________________________________
Right-Handed
80%
b) Why would you use a circle graph to show these data?
________________________________________________________________________
c) What other type of graph could you use to show these data? ________________________
Give 1 reason for your answer.
________________________________________________________________________
21
20
19
18
17
16
15
14
13
12
11
0
Comedy Show Ratings
Laughing Out Loud
Open Mike Comics
Rating (%)
Rating (%)
11. Two television comedy shows want advertisers to buy commercial time during their shows.
The 2 graphs show the ratings for each comedy show.
1
2
3
Season
Graph A
4
17.5
17
16.5
16
15.5
15
14.5
14
0
Season 4 Ratings
Laughing Open Mike
Out Loud Comics
Comedy Show
Graph B
a) What information about ratings does each graph show?
Graph A: _________________________________________________________________
Graph B: _________________________________________________________________
b) If you were going to buy commercial time to show your product, which show would you
buy time for? Why?
_________________________________________________________________________
Chapter Review ● MHR 43
Name: _____________________________________________________
Date: ______________
1 Practice Test
For #1 to #3, circle the best answer.
1. Which type of graph is best for comparing 1 category of data against the whole data sample?
For example, you are comparing the number of grade 8 girls to everyone in the school.
A line graph
B circle graph
C bar graph
D pictograph
2. Which type of graph is best for comparing the number of boys and the number of girls born in
each month of the year?
A double bar graph
B 2 circle graphs
C double line graph
D 2 pictographs
3. Energy bars cost 25¢ in 1985, 50¢ in 1995, and 75¢ in 2005.
Look at the graph. How is it misleading?
B The 2005 bar is 3 times
taller than the 1985 bar.
C The width of the bars
is different.
D The scale starts at 0.
Cost ($)
A The intervals on the
vertical (↕) scale are
not equal.
Cost of Energy Bars
Triples in 20 Years
1.00
0.75
0.50
0.25
0
1985
1995
2005
Year
4. The graphs show population data for selected provinces.
b) Which graph best shows that Alberta’s population
is almost 3 times more than Manitoba’s population?
Give 1 reason for your answer.
______________________________________
______________________________________
44
MHR ● Chapter 1: Representing Data
Population in 2006
Population in 2006
(9 520 500 people)
Saskatchewan
10%
Alberta
35%
Manitoba
12%
Co Br
lum itis
b h
M ia
an
ito
ba
Sa
sk
atc
he
wa
n
______________________________________
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Al
be
rta
______________________________________
Population (millions)
a) Do both graphs provide the same information?
Give 1 reason for your answer.
Province
British Columbia
43%
Name: _____________________________________________________
Date: ______________
5. Brenden surveyed the grade 8 students to find out their choice for the year-end field trip.
The table shows his results.
Activity
Bowling
Picnic
Inline skating
Movie
Votes
17
20
15
10
Draw a bar graph to show the data.
ˆ Give the graph a title.
ˆ Label the x-axis “Activity.”
Write the categories for Activity under
the x-axis.
ˆ Label the y-axis “Number of Votes.”
ˆ Mark the intervals on the y-axis from
0 to 20.
ˆ Draw bars for each activity.
6. Jasmine surveyed 100 grade 8 students about their favourite ways to spend time.
a) Write 2 conclusions you can make from the graph.
Favourite Ways to Spend Time
________________________________________
Other
________________________________________
Reading
________________________________________
c) Is the graph misleading? Circle YES or NO.
Explain.
________________________________________
________________________________________
Activity
b) Make up a more descriptive title for the graph.
Internet
Video or
Computer Games
Sports
Television
0
5
10
15
20
25
30
Number of Students
d) Name 1 other type of graph that could be used to show
these data.
e) Give 1 advantage or disadvantage of using a different type of graph to show the data.
_________________________________________________________________________
_________________________________________________________________________
Practice Test ● MHR 45
Name: _____________________________________________________
Date: ______________
Imagine you are a reporter for a school newspaper.
Look in newspapers, magazines, and on the Internet for information about the music industry to
show in a graph.
a) Complete the table to show your data.
Artist or Group
Example:
Nickleback
Research Topic
Monthly sales of their album
Dark Horse
Data Collected
November: 60 000 sold
December: 30 000 sold
b) What is the best type of graph to use to show your data?
Give 1 reason for your answer.
_________________________________________________________________________
c) Draw a graph using your data.
d) How could you change your graph to make it misleading?
_________________________________________________________________________
46
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
Date: ______________
Unscramble the letters of each term.
Use the clues to help.
A
14
12
10
8
6
4
2
0
B
OBLUDE RBA PAHRG
Zoe
Matt
hn
olo
gy
Hi
s to
ry
Sc
Te
c
ien
ce
Sp
Fic
t
or
ts
ion
Number of Books
1.
Zoe’s Books and Matt’s Books
ABR HARPG
olo
Sc
ien
Te
c
hn
Hi
sto
ry
ts
or
Sp
Fic
t
ce
gy
Zoe’s Books
14
12
10
8
6
4
2
0
ion
Number of Books
2.
3. general direction in which a line graph is going
DETNR
4.
IENL ARGHP
Whitehorse Average Maximum
Temperature
Temperature (°C)
20
15
10
5
0
–5
–10
–15
J
F M A M
J J
Month
A
S
O N D
5. change the appearance or twist the meaning of
something in a way that is misleading
SDITOTR
6.
IRCLEC RAHGP
Akira’s Week on Internet (20 h)
Surfing
13%
Homework
12%
Chat lines
50%
Watching
Videos
25%
7.
T-Shirts Sales
Monday
Tuesday
Wednesday
Thursday
Friday
PPAOCGTHRI
represents 10 T-shirts
8. spread between the smallest and largest numbers
ALNRVTEI
1200
1000
800
600
400
200
0
Population
Trends
ULBEDO ENLI ARHGP
Riverside
Hillview
200
2
200
3
200
4
200
5
200
6
200
7
9.
Population
in a range of numbers
Year
Key Word Builder ● MHR
47
Name: _____________________________________________________
Date: ______________
Math Games
The Plot Thickens
Play The Plot Thickens with a partner.
• 2 dice per pair of students
Rules:
• Each player rolls 1 die to decide who will play first.
If there is a tie, roll again.
• Players take turns rolling 2 dice.
• After each turn, each player adds the values of the 2 dice.
Record the totals for each turn.
• The first player to roll the same total 5 times wins the round.
• The winner scores the total that he or she rolled 5 times.
• The player who loses a round plays first in the next round.
• The first player to reach 20 points wins the game.
In my first 4 turns, I rolled totals
of 7, 5, 11, and 7.
x
x
x
x
________________________________
2 3 4 5 6 7 8 9 10 11 12
1. Use your totals from The Plot Thickens to create a bar graph.
The total that I rolled 5
times was 6, so I scored
6 points for the round.
ˆ Give the graph a title.
ˆ Label the y-axis.
ˆ Label the x-axis.
ˆ Draw bars.
2. a) What is another way you could record your totals each time you roll?
_________________________________________________________________________
b) What type of graph would you create with the data collected in part a)?
_________________________________________________________________________
Give 1 reason for your answer.
_________________________________________________________________________
48
MHR ● Chapter 1: Representing Data
Name: _____________________________________________________
Date: ______________
Challenge in Real Life
Keep Your Community Green
Communities across Canada are concerned about the amount of garbage they produce.
As a result, many cities, towns, and schools have recycling programs.
Research how much waste is recycled in your school.
1. Survey your classmates to find out how many of each item they recycle in a week at school.
What kinds of questions could you ask?
• ___________________________________________________________________________
• ___________________________________________________________________________
• ___________________________________________________________________________
2. Fill in the data table. Separate your results into 4 or more categories.
Category
Number That Were
Recycled
Example: Containers ( juice boxes, water bottles, etc.)
15
3. What kind of graph would be best to show the data for the whole school?
____________________________________________________________________________
4. On a separate sheet of paper, make a graph that shows how much material is recycled
each week.
5. Name 2 or more ways that your graph might be misleading.
_____________________________________________________________________________
_____________________________________________________________________________
Challenge in Real Life ● MHR 49
Answers
d) You have to do calculations to find out what percent of his money
was spent on each item.
6. a) Circle graph: Shows the percent of time out of a total of 40 hours that
each person practises. Bar graph: Shows the number of hours each
person practises a week.
Get Ready, pages 2–3
1. 9
2. 4
3. 37%
4. July. Answers will vary. Example: The graph goes up, peaks, and then goes
down.
5. 150
Math Link
a) rap b) classical
Market Share (%)
c)
Market Share of Music Producers
35
30
25
20
15
10
5
0
Sony BMG
Universal
Warner
EMI
Music
Music
Group
Group
Group
Music Producers
Independent
Labels
b) Answers will vary. Example: Which 2 people together use 75% of
the practice time? Answer: Min and Ann
c) Answers will vary. Example: How much longer does Ann spend
practising than Sara each week? Answer: Ann spends 6 h more than
Sara each week.
7. a) Line graph: Shows the change of growth from week 1 to week 4.
Pictograph: Shows the height of the plant at the end of weeks 1, 2, 3,
and 4. b) weeks 3 and 4
c) You have to look at the row for each week to see how many leaves
have been added to the row. If the same number of leaves is added to
each row, the plant grew at the same rate.
d) It shows the rate of the change in the height of the plant more clearly.
e) It shows the height of plant after each week.
Decibels of Different Sounds
8. a)
160
Sound Level (dB)
1.1 Warm Up, page 5
1. a) circle graph b) 20% c) 25%
2. a) bar graph b) 24
3. a)
3
1
b)
4
3
140
120
100
80
60
40
20
0
Leaves Whisper Heavy Lawn Hockey Thunder Stock Balloon
Rustling
Traffic Mower Game Clap
Car
Pop
Races
4. a) 30, 35, 40, 45, 50, 55, 60 b) 0, 20, 40, 60, 80, 100, 120, 140
5. a) 0.55 b) 0.06
Type of Sound
6. a) 22% b) 3%
1.1 Advantages and Disadvantages of Different Graphs, pages 6–19
Working Example 1: Show You Know
b) A bar graph allows for an accurate comparison of sound levels.
c) NO. The data are not a comparison over time.
b) NO. A line graph would not be useful because you are not showing changes
in data over time.
d) YES. A pictograph could be used, but it would not be as accurate as
the bar graph because of the fractions of pictures that you would have
to use.
Apply
c) circle graph d) 75 more Fuji and MacIntosh apples
9. a) 10
a) The bar graph is easier to read because there are no calculations required.
b)
Working Example 2: Show You Know
Ari
Other
2. Answers may vary. Example: Bar graph, because it shows the number of
votes for each game. Example: Circle graph, because it shows the percent of
votes for each type of game out of a total of 60 votes.
3. Answers may vary. Example: They are similar because they both include
categories.
4. Answers may vary. Example: They are different because 1 shows
information using bars, and the other uses pictures.
Practise
5. a) $10
b) The pictograph. Each symbol represents $10 and no partial symbols are
used.
c) The circle graph. It is easy to see that half the circle is made up of food
and clothing.
MHR ● Chapter 1: Representing Data
11. a) Answers may vary. Example: A double bar graph.
b) The double bar graph shows a comparison of the 2 schools across
the 4 different categories.
c) entertainment news and music downloads d) no
e)
50
45
40
35
30
25
20
15
10
5
0
Web Site Features Students Prefer
Queen Elizabeth
Hillside
inm
Ne en
ws t
wn M
loa usic
ds
Co
nt
es
ts
M
es
s
Bo ag
ar e
ds
1. DOUBLE LINE GRAPH. It most clearly shows the changes in ticket sales
over 6 weeks.
b) A bar graph or a circle graph would be a better choice.
Do
Communicate the Ideas
Bai Niki Tuong
Grade 8 Member
10. a) A line graph is best for showing changes in data over time.
Number of Votes
Hockey
ta
Basketball Volleyball Soccer Baseball
Favourite Sport
b) Answers may vary. Example: The bar graph makes it easy to compare the
frequency across the categories.
50
Grade 8 Member
80
70
60
50
40
30
20
10
0
Number of Votes
Favourite Sports of Grade 8 Students
er
50
45
40
35
30
25
20
15
10
5
0
En
t
Frequency
a)
Feature
8. a)
Math Link
1.2 Warm Up, page 20
Score
1. a) It shows the types of video games preferred by 200 students.
b) It shows the favourite type of video games preferred by students.
c) bar graph
d) bar graph; The height of the bar shows the number clearly. With the circle
graph, you have to calculate the number of people.
2. No, because a line graph shows changes in data over time.
3. pictograph
1
b)
1
4
2
3
4
5
Quiz Number
6
Charles’s Math Quiz Scores
80
75
1.2 Misrepresenting Data, pages 21–30
Working Example 1: Show You Know
Score
4.
Charles’s Math Quiz Scores
100
90
80
70
60
50
40
30
20
10
0
1.–4. Answers will vary.
70
65
a) The vertical axis was drawn with a break in the scale that makes the decrease
in gas prices seem more significant than it is.
60
1
b) $1.19 c) $1.14
d) Use a continuous scale that starts at $0.00 and goes to $1.20 in increments
of 100¢.
Working Example 2: Show You Know
a) The symbols in the pictograph are not the same size, and they are not
spaced evenly.
2
3
4
5
Quiz Number
6
c) The bars appear to be increasing by a greater amount.
9. a) Health
b) Provincial Budget (2008–2009)
Transportation
8%
b) It appears that the same number of people prefer each of the lunch specials.
Health
27%
c) Draw symbols that are the same size and the same distance apart.
Other 4%
Energy
24%
Housing
Education 13%
24%
Working Example 3: Show You Know
a) The area of the large circle appears to be larger that the area of the small
circle, suggesting that the costs have greatly increased.
b) The cost in 2007 appears to be 4 times the cost in 2006, even though it is
actually only 2 times the cost.
Math Link
c) Use bars with the same width instead of circles.
1.3 Warm Up, page 31
Communicate the Ideas
1. a) Charlottetown: 5; Québec City: 7; Toronto: 4
1. a) The number of people surveyed is missing.
b) include the number of people surveyed; use a bar graph
a)–g) Answers will vary.
b) 16 students
c) by creating a break in the y-axis and therefore distorting the scale
d) 7 e) NO f) pictograph
2. Companies might want to distort data in their favour so people will think
their product is more popular than it really is.
2. The visuals should be the same size and spaced evenly apart.
Practise
3. a) 0
3. a) 3 b) 100
b) If it does not start at 0 and is not continuous, the y-axis can become
distorted.
c) It appears that candidate B received 3 times as many votes as candidate A,
even though B only received twice as many.
1.3 Critiquing Data Presentation, pages 3239
d) The scale is broken between 0 and 75.
Working Example: Show You Know
4. a) the Big Cheese, because it is larger
b) One is significantly larger than the other.
c) Use the same size of symbol for both burgers, and space the symbols
evenly apart.
5. a) Apples, because they have the longest line. b) APPLE GROWER
6. a) 2 b) twice as wide c) the horizontal scale has a break in it; Scott’s bar is
twice as wide as Bryce’s
Apply
7. a) that profits were 4 times higher in June
b) It is misleading because of the break in the y-axis.
Profits
600
500
400
300
200
100
0
d) It compares the percent of teens that picked a specific number of
baskets to the total number of teens.
e) Answers may vary. Example: The majority of teens picked 4, 5, or 6
baskets.
Communicate the Ideas
1. a) YES. The data can be easily counted and the symbols are
appropriate.
b) Answers may vary. Example: Yes, because the symbol for walking is
smaller than the symbol for biking or driving. Example: No, because
each symbol is approximately the same size.
c) NO. Ten is an easy number to count by.
d) Answers may vary. Example: A bar graph might be more accurate.
2. a) Answers may vary. Example: Danny is running faster each week.
y
e
Jun
ril
Ma
rch
Ap
Ma
rua
ry
b) The vertical scale has a break, which alters the way the graph shows
his running times.
Feb
Jan
ua
ry
Profit ($)
c)
a) 5 b) 3 c) 36%
Month
c) Use a continuous scale of 0 to 90 on the vertical axis, without a
break.
d) Profits are 2.5 times as high in June as they were in January.
Answers ● MHR 51
3. It is important to look at the type of graph used and think about whether it is
the best choice for displaying the data, how it is designed, and whether it
displays the data accurately.
8. a) NO
b) The number of cell phones and MP3 players is 58, which is more
than the number of computers.
Practise
4. a) She chose a double bar graph to compare each type of communication by
gender.
c) You could remove the break in the horizontal axis and use a scale
from 0 to 40, with intervals of 5.
9. a) Monday b) Wednesday c) 20
b) The graph is not misleading because the bars are the same width, and the
scale is uniform with no breaks.
d) Answers may vary. Example:
Number of Lockers Rejected
c) Answers may vary. Example: More girls use the Internet than boys.
Monday
d) It would be misleading because the data do not show changes over time.
5. a) Answers may vary. Example: More grade 9 students than grade 8 students
spend less than 1 hour on the Internet.
Tuesday
Wednesday
b) A comparison of time spent on the Internet by the 2 grades can be shown
on 1 graph.
Thursday
Friday
c) Two circle graphs could be used to show the percent of students in each
grade that used the Internet for each time interval.
6. a) Answers may vary. Example: 18 cars in the parking lot were sedans.
b) A circle graph shows a comparison of each car type as a percent of the
total number of cars. c) 50 d) 8% e) 4 out of 50 cars
represents 10 lockers
10. a) The majority of students are right-handed. There are approximately
as many left-handed students as there are ambidextrous students.
b) A circle graph shows the percent of students in each category.
Apply
7. a)
c) A bar graph could be used because it would display the number of
students in each category.
11. a) Graph A: shows a comparison of the ratings in each season; Graph
B: shows a comparison of season 4 ratings only
b) Open Mike Comics because it seems to be growing in popularity,
while the popularity of Laughing out Loud is declining over time.
Al
pin
e
150
100
50
0
Snowboard Type
b) Answers may vary. Example: That the Freerider snowboard is twice as
popular as the Freestyle.
c) Using a bar graph makes it easy to compare the types of snowboards.
8. a) health b) bar graph
c) BAR GRAPH. It shows that health is almost twice as popular as the other
foundations.
9. a) It looks like blue is much more popular because of the break in the
vertical axis.
b) You could create a vertical scale that goes from 0 to 60, in intervals of
10 with no break.
c) He could use a circle graph to show the percent of each type of
calculator sold.
Practice Test, pages 44–45
1. B 2. A 3. C
4. a) Answers may vary. Example: Yes, they both provide the same
information. The bar graph shows the number of people in each
province; the circle graph gives the information as a percent of the
total population.
b) The bar graph, because the bar for Alberta is about 3 times the height
of the bar for Manitoba.
5.
Votes
Fre
es
tyl
e
Fre
er
ide
r
Fre
ec
ar
ve
Number
Snowboard Rentals
25
20
15
10
5
0
Year-end Field Trip
Survey
Bowling Picnic
Activity
Math Link
a) the percent each performer’s sales are of total sales during the
6-month period
Inline Movie
Skating
6. a) Answers may vary. Example: Using the Internet is the most popular
choice, and reading is the least popular choice.
b) the number of sales for each performer in each month of the 6-month period
b) Answers may vary. Example: Grade 8 Students’ Favourite Activities
c) Answers may vary. Example: Performer A. He or she seems to be gaining in
popularity, even though performer B has sold more albums.
c) NO. There is a continuous scale that starts at 0, and both axes are
labelled.
Chapter Review, pages 40–43
d) circle graph
1. circle graph 2. bar graph 3. pictograph 4. line graph
e) An advantage of using a circle graph is that the percent of votes for
each activity is shown, which makes it easy to compare the results.
5. double bar graph
6. a) bar graph
Wrap It Up!, page 46
b) The circle graph makes it easier to decide on how to spend $1000 because
it uses percents.
a)–d) Answers may vary.
c) fiction: $500; science fiction: $250; sports: $190; history: $60
1. double bar graph 2. bar graph 3. trend 4. line graph 5. distort 6. circle
graph 7. pictograph 8. interval 9. double line graph
7. Answers may vary. Example:
a) A bar graph could be used to display the population of western provinces
and territories.
b) A circle graph could be used to display how Greg spends his weekly
allowance of $20.
c) A double bar graph could be used to display the number of boys and girls
in grade 7 and grade 8 at a school.
d) A line graph could be used to display the temperature change over a
month.
52
MHR ● Chapter 1: Representing Data
Key Word Builder, page 47
Challenge in Real Life, page 49
1.–5. Answers may vary.