3.1 Organizing and
You will need
• grid paper
• a ruler
Presenting Data
GOAL
Organize and present data to solve problems and make decisions.
Learn about the Math
On July 15, 2004, the city of Peterborough, Ontario,
declared a state of emergency due to flooding.
Approximately 191 mm of rain had fallen in 24 h,
causing an estimated $110 million in damages.
Jude and Samantha are writing an article for the school
newspaper about fundraising efforts to help flood
victims. They want to compare the amounts earned by
different fundraising events, so they researched past
fundraising events held at their school.
Fundraising event
bake sale
book sale
raffle
car wash
silent auction
garage sale
sponsored 10 km run
bike-a-thon
concert
talent show
donations
CD sale
winter carnival
Amount
raised ($)
75
128
320
65
156
284
680
300
2500
1250
473
145
411
Fundraising event
jellybean count
walk-a-thon
battle of the bands
pledges
sponsored community service
swim-a-thon
bingo
international dinner
scavenger hunt
charity ball
karaoke
recipe book
toy sale
Amount
raised ($)
188
390
670
433
225
240
175
135
105
1650
180
114
57
? Which type of fundraising event is most successful?
A. Organize the data into three or four categories. Choose a type of graph
(a bar graph, a pictograph, a line graph, a scatter plot, a stem-and-leaf
plot, or a circle graph) that would be appropriate to compare the
categories. Construct the graph.
B. What conclusions can you make from your graph?
92
Chapter 3
NEL
Reflecting
1. Why did you choose the type of graph you used?
2. What other way could you organize the data to determine which type
of fundraising event is most successful?
Work with the Math
Example: Organizing and analyzing data to look for a relationship
Is there a relationship between the amount of damage that is caused
by a flood and the amount of rain that fell?
Carina’s Solution
Amount of
Location rain (mm)
I used the Canadian Disaster Database
Web site for my information. I sorted
the data by year to find recent floods in
Canada. Then I looked for floods caused
by heavy rainfall in a short period of time.
I organized the information in a table.
Amount of damage
($ millions)
ON
450
40
AB
160
48
QC
155
93
Damage ($ millions)
Flooding Damage vs. Amount of Rain
Since I was looking for a
relationship between two variables,
I decided to construct a scatter plot.
I plotted flooding damage versus
amount of rain.
100
80
60
40
20
0
100
200
300
400
Amount of rain (mm)
500
I didn’t see any pattern in the data
points. They were all over the grid.
I cannot see a relationship between the amount of damage that is caused
by a flood and the amount of rain that fell.
A
Checking
3. Which type of graph (a bar graph, a
pictograph, a line graph, a scatter plot,
a stem-and-leaf plot, or a circle graph)
would you use to display the data for each
purpose below?
a) to predict the world’s population
growth in the future
NEL
b) to compare the percent of Canada’s
population with each blood type
c) to look for a relationship between the
number of hours your classmates watch
television and the number of hours they
play sports each month
d) to order NBA basketball players by
height
Collecting, Organizing, and Displaying Data
93
B
Practising
4. State the types of graphs that you could use
to present each set of data below. Which type
of graph do you think is most appropriate?
Data
Purpose of graph
a) temperature readings
to look for a trend
b) number of baskets
to compare player
performance
taken over five years
scored in one year for
five NBA players
c) percent of students
to predict the percent
with asthma each year of students with
over a 20-year period asthma in the future
d) types of garbage
to distribute resources
for recycling and
waste collection
e) number of games won
to determine if the
team’s performance
is improving
collected in one
community
by the Toronto Blue
Jays in each of their
first 25 years
5. This chart shows the estimated dog and cat
populations in several countries in 2002.
Gasoline
consumed
(L/100 km)
40
55
70
85 100 115
10.2 8.4 8.1 7.8 7.5 9.0 10.7
a) Construct a graph to show the relationship
between speed and gasoline consumed.
b) Use your graph to estimate the driving
speed that consumes the least amount
of gas.
c) At 100 km/h, 9.0 L of gas is needed to
travel 100 km. Use your graph to
estimate another speed at which 9.0 L
of gas is needed to travel 100 km.
d) Predict the amount of gas that is
needed to travel 100 km at 95 km/h.
7. Gerald’s Grade 8 class was surveyed about
snack preferences one month before and
one month after hearing a guest speaker
talk about nutrition.
Millions
of cats
61.1
76.4
Brazil
30.1
12.5
Preferred type
of snack
China
22.9
53.1
USA
25
Speed (km/h)
Millions
of dogs
Country
Before guest
speaker
After guest
speaker
potato chips
7
4
chocolate bar
9
3
apple
1
5
Japan
9.7
7.3
Russia
9.6
12.7
France
8.2
9.6
plain cereal bar
3
7
5
3
5
8
Italy
7.6
9.4
candy
Canada
3.9
6.8
carrot sticks
a) Construct the most appropriate type of
graph to compare the two types of pet
populations. Why did you choose this
type of graph?
b) How does your graph quickly show if
there are more dogs or more cats in a
country?
94
6. The speed that a car is driven affects the
amount of gasoline that the car consumes.
One car manufacturer recorded the following
gasoline consumption for a new model of car.
Chapter 3
a) Based on the data in the chart, did the
guest speaker convince students to eat
healthier snacks? Construct a graph to
support your answer.
b) Justify the type of graph you chose to
draw in part (a).
NEL
C
Extending
Age Wealth Age Wealth Age Wealth Age Wealth
8. a) Survey the students in your class about
their snack preferences, using the types
of snacks in question 7.
b) Organize your data in a chart. Then
display your data in a graph.
c) How do your results compare with the
results in question 7?
9. The September 7, 1992, issue of Fortune
magazine listed 233 billionaires and their
ages. The table shows the ages and wealth
(in billions of U.S. dollars) of the 60
wealthiest people in this list. Does the data
show a relationship between age and wealth?
50
88
64
63
66
72
71
77
68
66
68
67
71
54
62
37
24
14
13
13
11.7
10.0
8.2
8.1
7.2
3.5
3.4
3.4
3.4
3.3
69
36
49
73
52
77
73
62
54
63
65
50
64
57
86
7.0
6.2
5.9
5.3
5.2
5.0
5.0
4.9
4.8
4.7
3.0
3.0
3.0
3.0
3.0
23
70
59
96
84
40
60
77
68
83
69
58
71
55
66
4.7
4.6
4.6
4.5
4.5
4.5
4.3
4.0
4.0
4.0
3.3
3.3
3.2
3.2
3.0
68
40
62
69
49
64
83
41
78
80
71
68
68
54
68
4.0
4.0
4.0
4.0
4.0
3.9
3.9
3.8
3.8
3.6
3.0
3.0
3.0
3.0
2.8
CALCULATING A FRACTION
OF A WHOLE NUMBER
Suppose that you want to determine the number of slices in !3! of a 24-slice pizza. Because the
4
denominator of the fraction !3! is a factor of the whole number 24, you can use a shortcut.
4
First divide the whole number by the denominator, and then multiply by the numerator.
Example: Calculate !3! of 24.
4
Step 1: Calculate
1
!!
4
of 24 by dividing 24
Step 2: Multiply by the numerator, 3.
3
!! of 24 " 3 $ 6
4
" 18
by the denominator, 4.
1
!! of 24 " 24 # 4
4
"6
1
6
5
6
1. Use !! of 42 " 7 to calculate !! of 42.
2. Calculate.
3
a) !! of 15
5
NEL
3
b) !! of 12
4
3
c) !! of 48
8
4
d) !! of 55
11
Collecting, Organizing, and Displaying Data
95