568116 - Mathematics Study Guide Chapter 10 Statistics 1 The frequency distribution of a class of students according to hair colour is shown below.
Colour Frequency
Blonde 6
Chestnut 5
Black 12
Red 2
Which of the following graphs does not represent this distribution?
A) Distribution of students C) Distribution of students by hair colour by hair colour
B : 12 8 C : 4
N : B C N R
R :
Legend : 5 person
1 person
B) Distribution of students D) Distribution of students by hair colour by hair colour
12 R
8 B 4
N B C N R C 2 Canada sent 300 athletes to the Olympic games in Athens in 2004.
The table below shows the number of athletes in each category who went to Athens.
Canadian Olympic Team Number of Part of the whole Angle measure Category Athletes Canadian Olympic Team (Degrees) Rowing 30
Swimming 75 Other 90 team sports Other 105 individual sports Total 300
Complete the table and construct a circle graph to illustrate the given information.
Label each section of the graph appropriately. Show your work. 3 Sylvie asked 220 students for their favourite types of music.
Her results are recorded on the vertical bar graph below.
Unfortunately, she forgot one bar.
Favourite Types of Music Number of Students 70
60
50
40 ? 30
20
10
0 Rap Punk Rock Pop Alternative Types of Music
a) Construct the frequency table that was used to draw the bar graph above and include the missing numerical information.
Favourite Types of Music
b) Complete the bar graph by filling in the missing bar. 4 The following list shows the math marks obtained by students in a Secondary I class :
56 85 74 62 61 65 72 68 86 94 62
60 68 57 89 93 80 74 78 82 84 68
65 60 59 95 73 81 72 89 64 62 81
Complete the frequency table on your answer sheet.
5 Your Geography teacher posted the following graph to show the class results in January.
Geography Exam Results
7 6 Number of Students 5 4
3 2
1
30 40 50 60 70 80 90 100 %
From the graph, fill in the frequency table on your answer sheet. 6 The province of Quebec sent 100 participants to the Canadian Mathematics Competition. The ages of the participants vary from 12 to 19 years old.
Construct a frequency table to show the distribution of students according to age.
18 19 17 18 19 18 17 18 16 14 13 17 18 15 19 17 17 16 12 14 16 18 15 19 15 15 16 16 13 16 16 16 16 15 15 19 17 16 19 15 16 16 16 15 13 16 18 15 17 17 15 13 16 16 12 18 12 13 16 17 13 16 16 15 19 16 13 14 14 12 19 12 15 12 13 12 14 12 17 12 16 18 12 14 14 12 17 16 14 16
7 The ages of 30 Secondary I students are listed below. Using this data construct a frequency table.
12, 14, 12, 11, 13, 12, 12, 15, 13, 12, 13, 13, 13, 14, 12, 13, 12, 13, 13, 11, 13, 12, 12, 13, 12, 13, 13, 14, 12, 13.
8 The following is a list of the votes cast for Class President as they were read out by the scrutineer :
Paul Janet Henry Henry Lucy Henry Janet Lucy Paul Paul Henry Lucy Paul Lucy Henry Lucy Lucy Janet Janet Henry Janet Lucy Henry Paul Henry Janet Paul Janet Lucy Lucy
Complete the frequency table on your answer sheet for the foregoing data. 9 The following votes were cast for the top sports personality of the year in Quebec:
Gaétan Sylvie Gaétan Michel Michel Sylvie Guy Sylvie Gaston Sylvie Michel Guy Gaston Guy Sylvie Gaétan Sylvie Michel Sylvie Sylvie Gaétan Gaétan Guy Gaétan Guy Gaétan Michel Sylvie Sylvie Michel Gaston Michel
Complete the frequency table on your answer sheet for the foregoing data.
10 The list below represents the marks obtained on a French exam by the students in a Secondary I class.
95, 24, 78, 58, 89, 47, 36, 65, 69, 72, 42, 57, 68, 92, 64, 76, 75, 61, 58, 84, 31, 55, 67, 71, 78, 45, 68, 56, 91.
Using the foregoing data, complete the frequency table on your answer sheet. 11 Four days after the start of the Quebec Games at Baie-Comeau, many medals had already been awarded.
The following diagram shows the number of medals, by category, won by the 5 best-performing regions from the start of the games.
Number of medals by region
30
: gold medal 25 : silver medal : bronze medal
20 Number of medals 15
10
5
Regions
Using the data from the graph above, set up a table showing the total medals won by each region. 12 Daryl is treasurer of his school's student "Disco" Nights Profits council. The diagram on the right shows the profits that accrued from all the "Disco" $ Nights they held this year. 200 180 Set up the data chart that Daryl used to 160 construct this bar graph. 140 120 100 80 60 40 20 0 13 You want to avoid eating too much sugar this coming winter.
The diagram below will help you eliminate excess sugar from your diet.
Sugar Content of Several Food Products
Soft drink (10 oz)
Sugared cereal (1 cup)
Chocolate bar (32 g)
Cookies (4)
Flavoured drink crystals (8oz)
Legend : = one teaspoon
List these food products in order from the least sweet to the sweetest. 14 Vincent spent 26 hours watching television last week. His parent thought this was definitely too much. He claimed that his friends watched as much T.V. as he did.
Vincent asked his friends to keep track of the number of hours a day they each spent in front of the T.V. in a week.
Kristen Dean Andy
Days Hours Days Hours Days Hours
M 1 h 30 min M 3 h 00 min M 2 h 00 min T 3 h 30 min T 3 h 00 min T 2 h 30 min W 2 h 00 min W 3 h 00 min W 3 h 00 min T 3 h 30 min T 3 h 00 min T 4 h 00 min F 4 h 30 min F 5 h 00 min F 3 h 30 min S 7 h 30 min S 4 h 30 min S 6 h 00 min S 3 h 00 min S 6 h 00 min S 4 h 00 min
Tanya Phil
Days Hours Days Hours
M 4 h 00 min M 2 h 30 min T 3 h 00 min T 3 h 30 min W 2 h 00 min W 4 h 30 min T 3 h 30 min T 3 h 30 min F 4 h 30 min F 4 h 30 min S 5 h 30 min S 5 h 30 min S 6 h 00 min S 5 h 00 min
Tabulate the data that Vincent is going to show his parents. 15 A flower-box manufacturer's sales are represented in the bar graph below.
Flower Box Sales
Number of boxes
1st Wk 2nd Wk 3rd Wk 4th Wk 5th Wk 6th Wk Weeks
Set up a chart of the data he used to construct the foregoing graph. 16 The graph below shows how the student population is distributed among the various grades of a secondary school.
STUDENT POPULATION DISTRIBUTION OF A SECONDARY SCHOOL
NUMBER OF STUDENTS
300 280 260
240 220 200 180 160 140 120
Sec 1 Sec 2 Sec 3 Sec 4 Sec 5
GRADE LEVEL
Set up the data table that was used to construct this graph. 17 Francois works in a bicycle store. The graph below shows the sales for the period from March to September. Fill in the data table that was used to construct this graph.
Bicycles Sales (6 month period) Months
August July June May April March
5 10 15 20 25 Number of bicycles sold
18 The students in Michael's class were polled to find out what their favorite sports were.
All of their answers are listed below :
Hockey Hockey Baseball Soccer
Hockey Baseball Football Hockey
Football Hockey Baseball Hockey
Hockey Hockey Hockey Baseball
Hockey Hockey Baseball Hockey
Football Baseball Football Soccer
Football Soccer Baseball Football
Fill in the tally chart on your answer sheet. 19 The circle graph reveals the favorite sporting activities of 12 to 16 year-old students.
Favorite Sporting Activities of 12 to 16 Year-old Students
Swimming Skiing
Cycling Hockey
Baseball
Track and field
What percent of students prefer hockey? 20 This broken line graph shows the math class average for each of five terms.
What is the total number of terms for which the class average was above 60%?
Math Class Average for 5 Terms Class Average (%)
20 10 1 2 3 4 5 Term Number
21 Below are the total points for two NHL players over 6 seasons of hockey.
Season Doug Gilmour Steve Yzerman 1995 72 95 1996 82 85 1997 53 69 1998 56 74 1999 73 79 2000 38 52
Record the above data for each player in a broken-line graph. Make sure to label your graph well. 22 This summer, Dave's family is taking a vacation in the Gaspé. The table below shows the family budget for vacation expenses.
Gaspé Vacation Expenses
Expenses Cost ($) Portion of Expenses Degrees Hotels 4 000 Gasoline 1 500 Food 3 000 Other 1 500 Total 10 000 360°
Complete the chart above, and on the circle below draw a circle graph to illustrate the given information. Label the graph. 23 The graph below shows the number of shark attacks over a 10-year period.
World Wide Shark Attacks
90
s
k 80 c a
t 70 t A 60 k r
a 50 h S
f 40 o
r 30 e b
m 20 u
N 10 0 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Year
Which of the following statements is TRUE?
A) There were twice as many shark attacks in the year 2001 as there were in the year 1997. B) There were fewer shark attacks in the year 1997 than in the year 1992. C) The biggest drop in shark attacks happened between the years 1995 and 1996. D) The number of shark attacks decreased between the years 1998 and 2000. 24 A total of 298 hockey fans were surveyed to find out which was their favourite NHL hockey team. The results are recorded in the table below, but one number is missing.
Male Fans Female Fans Montreal 98 Toronto 57 24
What is the difference between the number of male and female fans who picked Montreal?
A) 21 C) 74 B) 62 D) 119 25 Céline surveyed her Secondary 1 classmates to determine their favourite types of movies.
Here are the results.
Survey Results of Favourite Types of Movies of Céline’s Secondary 1 Class Angle Measure Type Frequency (Degrees)
Comedy 6 Drama 4 Horror 6 Sci. Fi. 8 Total 24
Complete the table above and then construct a circle graph to illustrate this data. Label your graph.
26 The bar graph below shows the number of pets owned by students in a Secondary 1 class.
Pets Owned by Students in a Secondary 1 Class Number of Pets 12 10 8 6 4 2
0 Pets Cat Fish None Bird Dog Gerbil
Construct the frequency table that was used to draw the bar graph above.
Pets Owned by Students in a Secondary 1 Class 27 Joe's scores on four tests are shown on the graph below.
Joe's Test Scores Test scores 100
Test score
0 A B C D Tests
On which test did he score 80?
A) Test A C) Test C B) Test B D) Test D
28 The table below gives the final medal counts of five countries that took part in the Sydney Olympics.
Country Number of Medals United States 97 Russia 88 Britain 58 Canada 14 South Africa 5
Draw a bar graph to illustrate this data. Label the axes. 29 A class conducted a school survey about the type of shows students watch on television. The list below indicates the students' choices.
S Sports A Action C Comedies N News
C C N A A S C S C S N A S S C C A C A C S A N N S C S N A C A C N C C C A S C S A C C N N
Using this data, complete the tally and frequency table below.
30 In a survey, students in Secondary I were asked to name one favourite activity.
The results are shown in the circle graph below.
Music 8% Sports Reading 17% 4%
Dancing Video games 13% 21%
T.V. Internet 20% 17%
According to this circle graph, which of the following statements is FALSE?
A) Both sports and the Internet were chosen by the same number of students. B) More students like television than dancing. C) The three activities that students like the most are video games, the Internet, and sports. D) Dancing, television, and the Internet were chosen by half of the students. 31 A study of 300 Grade 7 students was made to determine their favourite foods. The results of the study are represented in the table below.
Number of Percent (%) Angle Measure Favourite Food Students of Total (in degrees) Pizza 180 60 Hamburger 75 25 Submarine 15 5 Other 30 10 Total 300 100
Draw a circle graph for the data above.
Grade 7 Students' Favourite Foods
32 Construct a circle graph using the information in the bar graph below.
Favourite Animals of Students in Class 132 at Minnow High
Animals
Dog
Ferret
Bird
Other
2 4 6 8 10 12 14 16 Number of Students 33 High school students were surveyed about their favourite sport.
The results of the survey are given in the table below.
Favourite Sports of High School Students
Sports Number of students Soccer 180 Hockey 150 Basketball 60 Football 30
Draw a bar graph to illustrate the survey results.
34 St-Félix zoo has 50 animal species divided by type and sub-group.
The Animals at St-Félix Zoo
Number of Type Sub-group Species Fresh water 11 Aquatic Salt water 9 Wild 12 Land Domestic 6 Migratory 5 Flying Non-migratory 7
What percent of the animal species are land animals?
A) 9% C) 24% B) 18% D) 36% 35 The following graph shows how Maryse spends her day doing different activities.
Time Spent by Maryse on Daily Activities
Resting Working 25% 30%
Exercising Travelling 7.5% 25% Socializing 12.5%
According to the graph, which one of the following statements is FALSE?
A) Maryse spends twice as much time resting as she does socializing. B) Maryse spends more time working than she does in doing any one of the other activities. C) Maryse spends 75% of her time doing activities other than work. D) Maryse spends as much time travelling as she does resting. Answer Booklet
1 [A] [B] [C] [D]
2 Canadian Olympic Team Number of Part of the whole Angle measure Category Athletes Canadian Olympic Team (Degrees) Rowing 30
Swimming 75 Other 90 team sports Other 105 individual sports Total 300
Canadian Olympic Team
3 a) Favourite Types of Music b) Favourite Types of Music Number of Students
70
60
50
40 ?
30
20
10
0 Rap Punk Rock Pop Alternative Types of Music
4 Math results Tally Frequency
55 - 69
70 - 84
85 - 99
5 Marks Tally Frequency
30 - 39
40 - 49 6 Age of Participants
Age Frequency
7 AGES OF SECONDARY I STUDENTS
AGES TALLY FREQUENCY
8 TITLE : ______
NAME TALLY FREQUENCY
9 NAME TALLY FREQUENCY
Gaétan
Michel
Gaston
Sylvie
Guy
10 DISTRIBUTION OF FRENCH MARKS
MARKS TALLY FREQUENCY
20 - 29
30 - 39
40 - 49
50 - 59
60 - 69
70 - 79
80 - 89 90 - 99
11
12
13 1. ______2. ______
3. ______
4. ______
5. ______
14
15 16 STUDENT POPULATION DISTRIBUTION OF A SECONDARY SCHOOL
17 Bicycles Sales
18 Sports Preferred by Michael's Classmates 19 ______%
20 The class average was above 60% for ______terms.
21 Total Points per Season
10
// 1995 22
Gaspé Vacation Expenses
23 [A] [B] [C] [D]
24 [A] [B] [C] [D]
25 Survey Results of Favourite Types of Movies of Céline’s Secondary 1 Class Angle Measure Type Frequency (Degrees)
Comedy 6 Drama 4 Horror 6 Sci. Fi. 8 Total 24
26 Pets Owned by Students in a Secondary 1 Class
27 [A] [B] [C] [D] 28 Final Medal Counts of Selected Sydney Olympics Participants 29 Favourite Shows
30 [A] [B] [C] [D]
31
32 Work
Animal Number of Fraction % Angle in students degrees Dog
Ferret
Bird
Other 20 Total 20 100% 360° 20
Favourite Animals of Students in Class 132 at Minnow High
33 Favourite Sports of High School Students
34 [A] [B] [C] [D]
35 [A] [B] [C] [D] Answer Section
1 B
2 Example of an appropriate solution Canadian Olympic Team Part of the whole Angle measure Category Athletes Canadian Olympic Team (Degrees) 30 1 Rowing 30 or or 0.10 or 10% 36 300 10 75 1 Swimming 75 or or 0.25 or 25% 90 300 4 Other 90 3 90 or or 0.30 or 30% 108 team sports 300 10 Other 105 7 105 or or 0.35 or 35% 126 individual sports 300 20 300 Total 300 or 1 or 1.00 or 100% 360 300
Canadian Olympic Team
Swimming
25%
Other team sports Rowing
30% 10%
Other individual sports
35% 3 a) Favourite Types of Music Frequency Types of Music (or number of students) Rap 45 Punk 25 Rock 60 Pop 50 Alternative 40 TOTAL 220
b) Favourite Types of Music Number of Students
70
60
50
40
30
20
10
0 Rap Punk Rock Pop Alternative Types of Music 4 Math results Tally Frequency
55 - 69 15
70 - 84 11
85 - 99 7
5 Marks Tally Frequency
30 - 39 1
40 - 49 3
50 - 59 5
60 - 69 7
70 - 79 6
80 - 89 4
90 - 100 2
6 Age of Participants
Age Frequency
19 8 18 11 17 11 16 27 15 13 14 8 13 10 12 12
7 AGES OF SECONDARY I STUDENTS
AGES TALLY FREQUENCY
11 2
12 11
13 13
14 3
15 1
8 VOTES FOR FOUR CANDIDATES
NAME TALLY FREQUENCY
Paul 6
Janet 7
Henry 8
Lucy 9 9 NAME TALLY FREQUENCY
Gaétan 7
Michel 7
Gaston 3
Sylvie 10
Guy 5
10 DISTRIBUTION OF FRENCH MARKS
MARKS TALLY FREQUENCY
20 - 29 1
30 - 39 2
40 - 49 3
50 - 59 5
60 - 69 7
70 - 79 6
80 - 89 2
90 - 99 3 11 Total number of medals by region
Number of Region medals
Quebec 67
Saguenay-Lac-St-Jean 33
South-Shore 32
Montreal 30
Estrie 20
- Accept any other pertinent title. - Do not count spelling mistakes. - The regions may be arranged in any order in the table.
12 DISCO NIGHT PROFITS
Theme Profits
Homecoming $80 Halloween $150 Christmas $20 Carnival $140 Easter $80 Spring $120
13 1. Sugared cereal 2. Cookies 3. Chocolate bar 4. Soft drink 5. Flavoured drink crystals 14 Number of Hours Spent Watching Television
NAME HOURS
Kristen 25.5 or 25 h 30 min Dean 27.5 or 27 h 30 min Andy 25 Tanya 28.5 or 28 h 30 min Phil 29
15 Flower Box Sales
WEEK NUMBER OF BOXES
1st week 150 2nd week 275 3rd week 250 4th week 400 5th week 300 6th week 175
16 STUDENT POPULATION DISTRIBUTION OF A SECONDARY SCHOOL
GRADE LEVEL NUMBER OF STUDENTS
Sec 1 260 Sec 2 180 Sec 3 210 Sec 4 200 Sec 5 120 17 Bicycles Sales
Month Number of bicycles sold
March 7
April 12
May 23
June 19
July 8
August 5
18 Sports Preferred by Michael's Classmates
Sport Tally Frequency
Baseball 7
Football 6
Hockey 12
Soccer 3
19 25 %
20 The class average was above 60% for 3 terms. 21 Example of an appropriate solution
Total Points per Season
100
90
80
Steve Yzerman 70
60
s t n i
o 50 P
l a t o T 40 Doug Gilmour
30
20
10
// 1995 96 97 98 99 2000 Season
Note: A legend could be used instead of names written inside the graph area.
Marking scheme: Correct scale on both axes Appropriate labels on both axes Correct plotting of data for Doug Gilmour Correct plotting of data for Steve Yzerman 22 Example of an appropriate solution
Expenses Cost ($) Portion of Expenses Degrees Hotels 4 4 000 or 40% or 0.4 144° 10 Gasoline 15 1 500 or 15% or 0.15 54° 100 Food 3 3 000 or 30% or 0.3 108° 10 Other 15 1 500 or 15% or 0.15 54° 100 Total 10 000 100% 360°
Food Hotels
Other
Gasoline
Gaspé Vacation Expenses
23 C
24 A 25 Survey Results of Favourite Types of Movies of Céline’s Secondary 1 Class Angle Measure Type Frequency (Degrees)
Comedy 6 90 Drama 4 60 Horror 6 90 Sci. Fi. 8 120 Total 24 360
Secondary 1 Class Favourite Types of Movies
Drama Horror
Comedy
Sci. Fi.
Note: Allowable margin of error ± 2. 26 Pets Owned by Students in a Secondary 1 Class Frequency Pet (or number of pets) Bird 2 Cat 10 Dog 7 Fish 5 Gerbil 2 None 6
27 C
28 Example of an appropriate solution
Country Final Medal Counts of Selected Sydney Olympics Participants
United States
Russia
Britain
Canada
South Africa 10 20 30 40 50 60 70 80 90 100 Number of Medals
The following criteria must be satisfied: 1. The axes must be correctly scaled. 2. The axes must be correctly labelled. 3. The bar graph must be correctly drawn and reasonably accurate. 29 Favourite Shows Type of Show Tally Frequency Sports 10 Comedies 17 Action 10 News 8
30 C
31 Example of an appropriate solution
Grade 7 Students' Favourite Foods
Pizza
Other
Submarine Hamburger 32 Animal Number of students Fraction % Angle in degrees 9 Dog 9 45% 162° 20 2 1 Ferret 2 or 10% 36° 20 10 6 3 Bird 6 or 30% 108° 20 10 3 Other 3 15% 54° 20 20 Total 20 100% 360° 20
Favourite Animals of Students in class 132 at Minnow High 10% 30%
Legend 15% Dog
Ferret
Bird
Other
45%
Marks are allotted on the basis of the following criteria: 1. Identification of the sections 2. Percents shown on graph 3. Correct size of angles 33 Favourite Sports of High School Students Number of students
180
150
120 90
60
30
0 Soccer Basketball Sports Hockey Football
Note: Accept a horizontal bar graph.
Marks are allotted on the basis of the following criteria: 1. The axes are labelled correctly. 2. The axes are scaled properly. 3. The graph is drawn correctly.
34 D
35 C