Name
10.1 Making Predictions
MATHPOWERTm
Eight,
pp. 312-313The results of a survey are often used to make predictions.
1. Monique surveyed 70 of the 700 students in her school to find out how many had CD players at home. She found that 45 of the students had CD players. How many students in the school would Monique predict to have CD players?
2. In a survey, 300 pet owners were asked what kind of pets they had.
Pet Ownership
Pet Frequency Percent
Dog 140
Cat 100
Bird 20
Fish 25
Other 15
a) Complete the table.
b) It is estimated that 65 000 pet owners live in a city. Predict the number of each type of pet in the city.
3. There are about 11 000 000 households in Canada. The table shows how many of every 75 households had certain appliances in their homes one year.
Home Appliances
Appliance Frequency Percent
Air Conditioner 18
Dishwasher 32
Clothes Dryer 55 Washing Machine 59 Microwave Oven 51
a) Complete the table.
b) Why do the percents not total 100%?
c) About how many Canadian households have each appliance?
4. A survey asked 450 grade 8 students which of the following activities they took part in last summer. The table gives the results of the survey.
Summer Activities Activity Percent Swimming Lessons 44% Camp 28% Summer Job 25% Summer School 23% Family Trip 58%
a) How many of the 450 students took part in each activity?
b) Why does the percent column total more than 100%?
c) Predict the number of students in your class that would have participated in each activity last summer. Conduct a survey to check your prediction.
Name
10.2 Collecting Data
MATHPOWERTm
Eight,
pp. 314-315Statistics is the science of collecting and organizing number facts. Data are usually collected from a sample. A sample is a selection from a population. A sample for a survey should be a random sample where each member of the population has the same chance of being chosen. If each member does not have an equal chance of being chosen, the sample
is a biased sample. A census is used to gather information from an entire population.
1. A survey was taken to determine which chores were most popular among teenagers. Each person was asked to list one favourite chore.
Favourite Chores
Chore Tally Frequency
Dusting *1
Vacuuming 1111 *1111 Doing Dishes 1111 1111 Mowing Lawn
1111 -IR*
Shovelling Snow1111 ***
Taking Out Garbage • IllMaking Bed ***1
a) Complete the tally sheet.
b) Which was the most popular chore?
c) How many people were surveyed?
2. Janelle conducted a survey to determine the number of children in each of her classmate's families. She recorded the results using these abbreviations: 0 one, T—two, R—three, M—more than 3.
OORT RR TROMOMMRT RRT T TRTRMOOROMR a) Complete a survey sheet for the data.
Number of Children in Families Number of
Children Tally Frequency
b) How many students were surveyed?
c) What was the most common number of rhildrPn?
d) How many families had more than two children?
3. State whether the following information would come from a census or a sample. a) Nineteen students in a grade 8 class have brown eyes.
b) The population of White Rock is 14 387.
c) There were 5 129 060 students enrolled in elementary or secondary school in Canada one year.
4. State whether the following samples would be biased.
a) Two hundred people at a beach were asked their favourite summer sport.
b) Every third person entering the shopping mall was asked his or her favourite make of car.
c) Every fourth person entering a Chinese food restaurant was asked to name his or her favourite food.
al !ion fn M 1Ii1 2 ql 11 12114 'I • 18 20 Name
10.3 Reading and Drawing Bar Graphs
MATHPOWERTm
Eight,
pp. 320-321A bar graph is used to compare things. The height of each bar on a bar graph shows the number of responses for that item.
1. The bar graph shows the number of players allowed to play each sport at one time.
1 5 a_ 2 6 3 • Sp
a) Which sport has the most players?
b) Which sport has the fewest players?
c) Order the sports from most to least in terms of number of players.
c) What is the difference between the population of Mexico City and Toronto?
d) What is the total population represented on the graph?
3. The table gives the heights of several of the world's highest cities, to the nearest hundred metres.
City Height
Bogota, Colombia 2600 Mexico City, Mexico 2300 Nairobi, Kenya 1800 Calgary, Canada 1000 Sao Paulo, Brazil 800 Edmonton, Canada 700
Display these data on a horizontal bar graph
or
2. The bar graph shows the population of eight world cities, to the nearest million.
ororro Tokyo Athens
4. The table shows the average length and height of five mammals found in Canada.
uny RUI y
New Yolk
—1vIontreal-x CO 7/
a) Which cities have approximately the same population?
b) What is the difference between the largest population and the smallest population?
Mammal Length (m) Height (m)
Grizzly Bear 2.6 2.8
Polar Bear 2.6 1.4
Lynx 0.9 0.6
Moose 2.8 1.7
Arctic Wolf 1.5 1.0
0 64 6 4 2 W f La ura s World ng 10 Hours
1. The graph shows the cost of unleaded gasoline, in cents per litre, over an 11-year period. Gasoline Cost 60 , 50 =7 40 V, cf, 30 20 10 0 1980 1982 1984 1986 1988 1990 1992 Year
a) Between which 2 years did the cost of gasoline decrease?
b) Between which 2 years did the cost of gasoline stay roughly the same?
c) Which year had the highest cost?
2. The table shows Canada's wheat and barley exports for 5 years.
Year Wheat Exports (million tonnes) Barley Exports (million tonnes) 1987 21 7 1988 24 5 1989 12 3 1990 17 5 1991 22 5
Display this information on a double broken-line graph.
Name
10.4 Reading and Drawing Broken-Line Graphs
MATHPOWERTmEight,
pp. 322-323A broken-line graph is used to show how something changes over a period of time.
3. The following table gives the percent distribution of electricity production in Canada by hydro, steam, and nuclear.
Electricity Production Year Hydro Steam Nuclear
1970 76.5 22.1 0.5
1975 74.0 20.8 4.3
1980 68.4 21.4 9.8
1985 67.4 19.1 12.8 1990 62.9 21.5 14.8 a) Display these data on a triple broken-line graph.
b) Which type(s) of production are decreasing?
4. The graph shows
the hours Laura worked at the gas station in one week. Compose and answer 3 questions about the graph.
Land Coverage by Continent Australia 5.2% Antarctica 8.9% Europe 7.2% 30% Africa 20.4% North America 16.3% South America 12% Name
10.5 Reading and Drawing Circle Graphs
MATHPOWERTmEight,
pp. 324-325Circle graphs are used to show how something is divided.
1. The circle graph shows the distribution of Canada's labour force in one year.
Canada's Labour Force Manufacturing
15.2% Agriculture Services 3.3%
4
34.8%.
Utilities 7.3% Trade 17.9% Other 14.9% Government 6.6%If the labour force that year was 13 513 000, calculate the number of people in each type of work.
a) Services b) Government
c) Manufacturing d) Utilities
e) Trade f) Agriculture
g) Other
2. The circle graph shows the percent of Earth's land covered by each continent.
a) Which 2 continents combined cover 50% of Earth's land?
b) Which 2 continents combined cover an area equivalent to South America?
3. Canada won 2 gold, 3 silver, and 2 bronze medals at one winter Olympics. Display these data on a circle graph.
4. The table shows the percent distribution of Earth's water area.
Source Percent of Earth's Water
Pacific Ocean 46.0% Atlantic Ocean 23.9%
Indian Ocean 20.3%
Arctic Ocean 2.6%
Other 7.2%
Display these data on a circle graph.
5. In one hockey season, the Edmonton Oilers won 38 games, lost 28 games, and tied 14 games. Display the team's statistics on a circle graph.
Name
10.6 Reading and Drawing Pictographs
MATHPOWERTm
Eight,
pp. 326-327A graph that uses pictures or symbols to display data is called a pictograph.
1. The pictograph shows the approximate number of elementary and secondary schools in 5 Canadian provinces.
Number of Schools New Brunswick
British Columbia :w: NA:: ,w. ::A.: 11.: Manitoba :w: NA:: ::A::
IF
Alberta MAcif :::::: pi ::iii1:. R pi R
.
Nova Scotia ii. . Each "A" represents 250 schools.
a) Approximately how many schools are in each province? New Brunswick British Columbia Manitoba Alberta Nova Scotia
b) Ontario has 5350 schools. How many symbols would be needed to represent this on the pictograph?
2. The table gives the number of points scored by 6 schools at a swim meet.
School Points School Points Mapleview 132 Balmoral 244 Parklawn 210 , Rosedale 96 Valleywood 185 Dewhurst 156 a) Round each number and display the data on a pictograph, using an appropriate symbol.
b) Compose and answer 2 questions about the graph.
3. The table shows the average monthly precipitation in Moncton, New Brunswick, from January to June.
Month Precipitation (mL) Month Precipitation (mL) Jan 125 Apr 90 Feb 99 May 84 Mar 112 Jun 90
a) Display the data on a pictograph, using an appropriate symbol.
b) Compose and answer 3 questions about the graph.
8. 2°C, -6°C, -6°C, 0°C, 1°C, 3°C, -1°C
Mean: Median:
Mode: Range:
9. The points scored by a school ski team during the past 8 competitions are listed.
219, 186, 170, 73, 175, 180, 73, 196 a) Find the mean, median, mode, and range.
Mean: Median:
Mode: Range:
b) Which measure of central tendency best represents the data? Explain.
10. The frequency table shows the marks on a math test.
Mark Frequency Mark Frequency
45 3 38 7
42 2 37 4
40 1 35 3
Find the mean, median, and mode.
11. The mean of the numbers 8, 12, 13, 15, 17, 19, and y is 16. Find y.
12. Write 5 numbers that have a) a mean of 12 and a median of 13
b) a mean of 9 and a mode of 10 Name
10.7 Mean, Median, Mode, and Range
MATHPOWERTm Eight, pp. 332-335The mean is calculated by finding the sum of the data and dividing by the number of pieces of data.
The median is the middle value when the data are arranged in numerical order. If the number of pieces of data is even, the median is the arithmetic average of the 2 middle values.
The mode is the number that occurs most frequently in a set of data. The mean, median, and mode are known as measures of central tendency. The range is not a measure of central tendency. It is the difference between the highest and lowest values in a set of data.
Is each statement always true, sometimes true, or never true?
1. If the mean, median, and mode are close in value, then these values describe the sample population fairly accurately.
2. There is more than one mode for a set of data.
3. The mean is a number that is not in the initial set of data.
4. The median best reflects the largest number of readers of a newspaper.
5. The mode best reflects your bowling ability
Find the mean, median, mode, and range for each set of data.
6. 15, 18, 16, 21, 18, 14, 12, 19, 11, 16
Mean: Median:
Mode: Range:
7. 80 min; 1 h, 65 min; 50 min; -3 h 4
Mean: Median:
Name
10.8 Stem-and-Leaf Plots
MATHPOWERTm Eight, pp. 336-337A stem-and-leaf plot gives a quick picture of a set of data. The first digit of each piece of data is the stem.
The second digit is the leaf.
1. The stem-and-leaf plot shows the number of nations represented at each Summer Olympics from 1952 to 1992. Number of Nations 3 0 2 5 6 7 7 7 4 9 5 7 6 4
a) Find the mean, median, and mode.
Mean: Median:
Mode:
b) What is the range of the data?
2. The stem-and-leaf plot shows the number of frost-free days in 20 Canadian cities.
Frost-Free Days 11 2 5 7 12 1 3 6 8 13 1 5 7 9 9 14 7 8 9 15 1 1 5 6 7
a) Find the mean, median, and mode.
Mean: Median:
Mode:
b) What is the range of the data?
c) How many cities have more than 155 frost-free days?
3. The list shows the number of days of snowfall per year for several Canadian cities.
66, 77, 60, 56, 55, 52, 55, 56, 74, 54, 54, 77, 54, 60, 51, 56, 83
a) Construct a stem-and-leaf plot.
b) Find the mean, median, and mode.
Mean: Median:
Mode:
c) How many cities have more than 60 days of snowfall per year?
4. The student marks for two math tests are shown.
1st Test 64, 72, 85, 76, 88, 67, 78, 59, 71, 73, 94, 92, 83, 79
2nd Test 66, 75, 88, 74, 92, 74, 82, 61, 67, 78, 92, 95, 86, 77
a) Display the data on a back-to-back stem-and-leaf plot.
b) How many students wrote each test?
c) What was the median mark for each test?
d) What was the range of marks on each test?
29 0 1 5 7 9 9
30 0 2 3 4 7 8 9 31 0 1 2 5 5 7
32
33 1 2
1. The heights of 26 grade 8 students are
• -1- 29 30 0 3. a 33 34 1 15 15 5 St idE 16 ' 0 nts 1.
,;
17 5 a his o (cm) Name10.9 Box-and-Whisker Plots
MATHPOWERTmEight,
pp. 338-339A box-and-whisker plot can be used to show the distribution of a set of data. To draw a box-and-whisker plot, you need to know the lowest value in the data, the highest value in the data, the median value of the data, the upper quartile,
and the lower quartile. These 5 numbers are known as a five-number summary. Stem-and-Leaf Plot Box-and-Whisker Plot
shown on the box-and-whisker plot.
ill
65
eig
What is the median height of the students?
2. The box-and-whisker plot shows the number of lifts for several ski resorts.
0
••
5 0 1 5 2a 25 3 0 Si Resert I iris
State whether each statement is true or false. Give a reason for your choice.
a) Fifty percent of the resorts have 5 or fewer lifts.
b) The range of the number of lifts of the top 75% of the resorts is 23.
c) The range of the upper quartile is 15.
a) The data are unevenly distributed, with more values around the lower end.
b) Most of the data are between the upper and lower quartiles.
c) The data are evenly distributed about the median.
4. The stem-and-leaf plot shows the results of a driver education test.
Driver Education Test Scores
5 3 3 8
6 0 2 3 3 4 7 1 2 2 6 7
8 0 0 4 5 6 7 9 9 1 1 4
d) One-quarter of the ski resorts have more Draw a box-and-whisker plot to represent
than 8 lifts. the data.
3. Place the number of the box-and-whisker plot that best describes each statement in the blank.
3. Spin the spinner.
0
rol
u
FT1
rcl
In questions 1-5, list the possible outcomes of each experiment. If the outcomes are not equally likely, circle the most likely outcome.
6. Draw a tree diagram to find the possible outcomes.
a) Spin each spinner.
JILL.L L Li LC J}/11 Ll LC1.
1
1.
2. Toss a coin and roll a die.
4. Choose one letter without looking.
b) Toss a quarter and spin each spinner.
7. a) List the possible outcomes when you roll 2 dice.
b) How many possible outcomes are there?
c) How many possible outcomes total 5?
d) What total happens most often? In how many ways does it happen?
e) What totals happen least often?
5. Spin the spinner
and roll a die.
Name
10.10 Possible Outcomes
MATHPOWERTm Eight, pp. 340-341
Possible outcomes refer to all the possible results of an experiment. When you flip a coin, the possible outcomes are head and tail. The possible outcomes are sometimes called the sample space. Equally likely outcomes have the same chance of occurring. You can use a tree diagram to help you list the possible outcomes.
6. Choose one card without looking and state the following probabilities.
a) P(6)
b) P(odd number) c) P(number less than 4) d) P(2 or 7)
e) P(10)
f) P(factor of 8)
7. Jonah has a set of alphabet blocks. If he puts them all in a bag, what is the probability of pulling out each of the following?
a) an F b) a P
c) a consonant d) a vowel
8. A bag contains 9 black marbles, 6 green marbles, and 5 red marbles. If you choose one marble without looking, what are the
following probabilities? Express the probabilities as percents.
a) P(black) b) P(green) c) P(red)
d) P(red or black) 9. Use the spinner in question 2.
a) Give an example of an impossible outcome. b) What is the probability of an impossible outcome?
c) Give an example of a certain outcome.
d) What is the probability of a certain outcome?
PR
5 6 7[i
-
1 2 Name10.11 Probability
MATHPOWERTm Eight, pp. 342-343The probability of an event, P — number of favourable outcomes total number of possible outcomes •
In questions 1-4, find the probability of each event.
1. Choose 1 marble from the bag.
a) P(R)
b) P(G) c) P(B)
2. Spin the spinner. a) P(5) b) P(10) c) P(15) 3. Roll a die. a) P(1) b) P(2 or 3) c) P(even number) d) P(less than 4) 4. Toss 2 coins. a) P(H, H) b) P(at least 1 H) c) P(1 H, 1 T) 5.
a) List the possible outcomes for the spinner.
b) Find P(1).
c) Find P(even number).
4. What is each probability as a percent? a) P(1, D) b) P(2, B) c) P(1, A, B, C, D, or E) d) P(odd number, D) e) P(4, vowel)
f) P(oven number, consonant) g) P(odd number, vowel)
5. Complete the table to show the products of the outcomes. Outcomes of Spinner X 0 2 4 6 8 1 0 2 4 6 8 2 0 4 8 12 3 4 5 6
6. What is each probability as a percent rounded to the nearest whole?
a) P(a product of 2) b) P(a product of 8) c) P(a product of 0) d) P(an even product) e) P(an odd product)
f) P(a product greater than 15) P(a product less than 25)
h) P(a product that is a perfect square)
For questions 5 and 6, the die is tossed and the spinner is spun.
coin
Name
10.12 Independent Events
MATHPOWERTm Eight, pp. 348-349Events are independent if each outcome has no effect on the others.
For questions 1 and 2, a coin and a die are tossed.
1. Complete this tree diagram to show all the possible outcomes.
Die 1 2
2. What is the probability of each outcome as a fraction in lowest terms?
a) a head and 3
b) a tail and an even number c) a head or tail and 5
For questions 3 and 4, these spinners are spun.
3. Use a tree diagram to find all the possible outcomes. List them here.
Outcomes H, 1 H,2
1. The chart shows the amount of protein in a single serving of several foods.
Food Protein (g) Cottage Cheese 17 Spinach 3 Pumpkin Pie 6 Chicken Pie 23 Tomato Soup 7
2% Partly Skimmed milk 15
Potato Salad 5
Liver 15
Display these data on a horizontal bar graph.
IN=
2. The chart shows the average daily
temperatures for one week in London, Ontario.
Temperature Temperature Day (°C) Day (°C) Mon. 15 Fri. 20 Tues. 12 Sat. 18 Wed. 17 Sun. 16 Thurs. 21
Display these data on a broken-line graph.
•
IMM
6. Spin the spinner and roll the die.
• • • • • • a) List all the possible outcomes.
b) Find P(B, 6).
c) Find P(R, even number).
d) Find P(B or Y, odd number). Sports Viewing Hockey 25% Basketball 15% Tennis 5% Other 10% Baseball 35% 'Football 10% Name
Test One CHAPTER 10: Statistics and Probability
MATHPOWERTm Eight, pp. 309-3534. Find the mean, median, mode, and range of each set of values.
a) 29, 27, 23, 28, 30, 23, 28 Mean: Median: Mode: Range: b) 67, 49, 83, 60, 79, 49 Mean: Median: Mode: Range: c) 43, 74, 75, 57, 85, 32 Mean: Median: Mode: Range:
5. The maximum speeds for some animals are given, in kilometres per hour.
Animal Speed (km/h) Animal Speed (km/h) Cheetah 113 Elephant 40 Wildebeest 80 Hyena 64 Elk 72 Greyhound 63 Giraffe 51 Zebra 64
Coyote 69 Grizzly Bear 48 Display the data on a box-and-whisker plot.
3. The circle graph shows the results of a survey that asked students for their favourite sport to watch on television.
In a school population of 420 students, how many chose each sport?
a) Baseball b) Hockey
c) Football d) Basketball e) Tennis f) Other
Name
Test Two CHAPTER 10: Statistics and Probability
MATHPOWERTm Eight, pp. 309-3531. The chart shows the number of calories in a single serving of several foods.
Food Calories Brown Rice 100 Pea Soup 145 Skimmed Milk 90 Orange Juice 110 Egg 80 Pancake 60 Roast Turkey 200
Display this information on a bar graph.
2. The number of medals won by several countries at the 1992 Summer Olympics is given.
Country Number of Medals
China 54 Cuba 31 Hungary 30 South Korea 29 France 29 Australia 27 Spain 22 Britain 20 Italy 19 Canada 18
Display the data on a box-and-whisker plot.
4. Find the mean, median, mode, and range of each set of values.
a) 119, 123, 107, 112, 99, 120, 107 Mean: Median: Mode: Range: b) 34, 41, 40, 38, 43, 40, 41, 34 Mean: Median: Mode: Range: c) 149, 206, 164, 158, 197, 191 Mean: Median: Mode: Range:
5. The list shows the average number of wet days per year in several Canadian cities. 120, 121, 113, 108, 120, 156, 137, 156, 102, 107, 133, 103, 121, 131, 152, 104
a) Construct a stem-and-leaf plot.
b) Find the mean, median, mode, and range.
6. Spin each spinner.
a) List all the possible outcomes.
3. Jarrod spent last Saturday doing the following activities. Sleeping: 10 h, Eating: 2 h, Shopping: 2.5 h, Reading: 1.5 h, Watching TV: 3 h, Doing
Homework: 2 h, Playing Outside: 3 h
b) Find P(4, C).
c) Find P(even number, vowel). d) Find P(odd number, consonant).
T1 Me
Name
Extension CHAPTER 10: Statistics and Probability
MATHPOWERTm Eight, pp. 309-353
The graphs show the value, in millions of dollars, of the commercial, industrial, and institutional building permits in one city for the years 1993 and 1994. COMMERCIAL
Total value
1993 MIMI $34.82
1994 $26.11
INDUSTRIAL INSTITUTIONAL
Total value Total value
1993 I$3.66 1993 $42.93
1994 $18.3 1994 $40.66
1. By how much did each type of building permit increase or decrease from 1993 to 1994?
2. The value of residential building permits in 1993 was $86.71 million and in 1994 was $72.9 million. Draw a graph to show the total value of all building permits for 1993 and 1994.
3. To the nearest hundredth, what percent of the 1993 total value is the 1994 total value?
The graph shows the path followed by a flag being raised on a flag pole.
25 20
a)
(e)
4. Explain what happened at 0 s.
5. Describe in your own words what happened to the flag as shown in the graph.
6. What is the height of the flagpole?
7. What was the average speed at which the flag was raised?
8. a)
Find the mean of each set of numbers. 0.35, 3.5, 35 b) 1 2 -5 c) 05 -3 125
4' 3' 6 ' 4' 2-1 10
9. Write the median number between each pair.
1 5
a) 20 and 36 b) 0.6 and 2.4 c) and
4 12
10. The mean of two numbers is 15. One number is -4. What is the other number?
11. Write 9 numbers with a mean and median of 4.
12. Bushra used letter cards to make the word PROBABILITY. She laid them face down on the table. If Bushra turned over 1 card at a time, what is the probability that she would turn over
a) a B? b) a P?
c) a vowel? d) a consonant? If 2 cards were turned over at once, what is
the probability of turning over
e) the same 2 letters?
13.
i
iii
" a) Construct a broken-line graph to show the surface area when 1-cm linking cubes are joined side by side as shown.b) Use your graph to predict the surface area of 25, 50, and 100 cubes.
