Data ManagementU N I T

• Text• interpret and evaluate data intables and graphs

• draw labelled graphs by handand with a computer

• recognize accuracy or bias intables and graphs

• examine how data werecollected and if they arereasonable

• find the mean and the mode of a set of data

• predict the results of a survey• design and conduct a survey

Learning Goals

154

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Students collected data about the amount of rainfall.

range

mean

average

mode

intervals

line graph

sample

bias

Key Words

• In which month did the most rain fall?

• In which month did the least rain fall?

• How else could you display the data?

• How do you think these data were collected?

• What other weather data might you record?

155

Monthly Rainfall for One School Year

Month Amount (mm)

September 70

October 63

November 67

December 62

January 47

February 46

March 58

April 65

May 67

010203040506070

Monthly Rainfall for One School Year

Months

Sept

embe

rOct

ober

Nove

mber

Dece

mber

Janu

ary

Febr

uary

March

April

May

Rain

fall

in m

illim

etre

s

Document1 14/7/04 9:45 AM Page 155

Interpreting Data

L E S S O N

156 LESSON FOCUS Read and interpret data in tables and graphs.

Governments and organizationscollect and use data to help make decisions.Before a decision is made toredesign a park, data are collectedon its current use.

Which activity has the most participants?Write 5 other things you know from the data.What do the data not show?Do the table and the circle graph show the same data? How do you know?How might the data have been collected?Do you think the data are reasonable? Explain.

Show and Share

Write a question that can be answered from the data.Exchange questions with another pair of classmates.Answer your classmates’ question.

Fun Times Park Saturday Activities

Activity Number of People

Bicycling 112

Rollerblading 93

Running 35

Riding scooters 51

Skateboarding 43

Saturday Activities at Fun Time Park

Skateboarding

Running

Rollerblading

Bicycling

RidingScooters

If we subtract the least value from the greatest, we find the range of the data. It tells how

spread out the data are.

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157

Fun Times Park rents equipment.The rental data are displayed in graphs.

Tables, pictographs, bar graphs, and circle graphs each show data in an organized way.The title of the graph tells you what data are displayed.Each graph presents the same data.

➤ In a pictograph, symbols show the data.A key shows what each symbol represents. In the pictograph,

represents 20 rentals.

To find the number of scooters

rented, count the

and multiply by 20.

There are 8�12� .

8 � 20 = 160

represents 10 rentals.

160 + 10 = 170So, 170 scooters were rented.

➤ In a bar graph, bars show the data.The numbers on the vertical axisshow the scale.In this bar graph, the bar for rollerblade rentals is about halfway between 220 and 240.So, the rollerblade rentals are about 230.From the bar graph, the greatest number of rentals is 230.The least number of rentals is about 150.So, the range is about 230 – 150,or about 80.

Equipment Rentals for Week of July 2

Type

of E

quip

men

t Rollerblades

Bicycles

Skateboards

Scooters

= 20 People

020

Equipment Rentals for Week of July 2

Type of Equipment

Rolle

rbla

des

Bicy

cles

Skat

eboa

rds

Scoo

ters

Num

ber o

f Ren

tals

406080100120140160180200220240

Number Strategies

Write an equivalent decimal foreach number.

• 0.3• 1.9• 2.60• 9.80• 6.5

Numbers Every Day

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158

1. Look at this table of weather data in Canada.a) Which city has

the most wet days? The fewest?

b) Which city has the greatest snowfall? The least?

c) Which cities have about 3 times as much precipitation as Calgary?

d) Write 2 other questions that can be answered from the data.Answer the questions.

e) Describe other ways you could display these data.

2. The circle graph shows the after-school activities students chose at Allgood Elementary School.a) Which activity was chosen

by the most students? The fewest?

b) Estimate the fraction of students that chose the homework club.

c) Which 2 activities were chosen by about the same fraction of students?

➤ In a circle graph, data are shown as parts of a whole.This circle graph shows the same data as in the pictograph.The sector for bicycle rentals is about �

14� of the circle.

About �14� of the people who rented

equipment rented bicycles.

Students Taking Part in After-School Activities

ChoirHomework

ClubComputerClub

Dance andFitness ClubScience

Club

Average Annual Precipitation in Canadian Cities

City Snowfall Total Wet (cm) Precipitation Days

(mm)

Charlottetown, PE 338.7 1201 177

Quebec City, QC 337.0 1208 178

Ottawa, ON 221.5 911 159

Calgary, AB 135.4 399 111

Vancouver, BC 54.9 1167 164

Victoria, BC 46.9 858 153

Equipment Rentals for Week of July 2

Skateboards

Rollerblades

BicyclesScooters

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ASSESSMENT FOCUS Question 4

3. This pictograph shows the number of days Members of Parliament (MPs) sat in the House of Commons in one year.a) What months are not shown?

Why do you think they are not shown?b) How many days did MPs sit in

the House of Commons in March?c) How many days did MPs sit during the year?d) Suppose the graph was redrawn with this key.

= 8 days

How would the graph change?

4. This bar graph shows the number of days vegetables grow before they are picked.a) Which vegetable takes

longest to grow?b) What is the range of the data?c) Suppose you wanted to

display these data as a pictograph.What key would you use? How many symbols would you need for each vegetable?

Which do you find easier to read:a graph or a table? Explain. Look through newspapers and

magazines, or search the Internet. Find a table of data you can graph. Graph the data. Give reasons foryour choice of graph.

159

When parliament meets,we say “MPs sit in theHouse of Commons.”

Days MPs Sitin the House of Commons

January

February

March

April

May

June

September

October

November

December

= 4 days

020

Number of Days Vegetables Growbefore Harvesting

Vegetable

Cabba

geLe

ekLe

ttuce

Oni

on

Num

ber o

f Day

s

406080100120140160

Spin

ach

Peas

Turn

ip

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L E S S O N

Mean and Mode

160 LESSON FOCUS Calculate the mean and the mode of data.

You will need 12 counters.

Three friends took part in a Read-A-Thon.One month, Ali read 2 books,Bryn read 3 books,and Lynne read 7 books.

Use counters to represent the number of books.Find one number that best represents the number of books each person read.

Show and Share

Share your findings with a classmate.How did you use counters to help you decideon the number?Explain to your classmate why your numberrepresents the data.

The range of a data set tells how spread out the data are.These sets all have range 5.

3, 4, 5, 6, 7, 8 3042, 3047, 3045 586, 583, 581, 582

The range does not tell us what kinds of numbers are typical.In this lesson, you will learn other ways to find one number to represent all the numbers in a data set.

Mental Math

Estimate each sum ordifference.

5.39 + 4.411.97 – 0.687.63 + 10.015.92 – 2.986.54 + 1.11

Numbers Every Day

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161

The mean is a number that represents the centre of a set of numbers.It is the balance point of the numbers.

Mary surveyed 4 friends on the number of first cousins each has.She used linking cubes to represent the number of cousins.

➤ One way to find the mean is to make rows of equal length.

The mean number of first cousins is 5.

When you make equal rows or columns,the total number of cubes does not change.You can use this total to calculate the mean.

➤ The number of cubes in each row is 3, 4, 4, 9.Add these numbers together: 3 + 4 + 4 + 9 = 20Then divide by the number of rows, 4: 20 � 4 = 5

The mean is 5.

The mode is the number that occurs most often in the data.

➤ To find the mode, determine which answer occurs most often.In Mary’s data, the number 4 occurs twice.The mode is 4 cousins.Two people have 4 cousins.

Both the mean and the mode aresometimes called

the average.

Ahmed

Maria

Luis

Marlyn

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162 ASSESSMENT FOCUS Question 5

What is the difference between mean and mode? Use a set of data to explain.

1. Use linking cubes to find the mean of each set of data.a) 3, 4, 4, 5 b) 1, 7, 3, 3, 1 c) 2, 2, 6, 1, 3, 4

2. Calculate the mean of each set of data.a) 2, 4, 7, 4, 8, 9, 12, 4, 7, 3 b) 24, 34, 44, 31, 39, 32

3. Here are the weekly allowances of 10 Grade 5 students:$4, $6, $8, $10, $15, $5, $7, $10, $5, $10a) What is the mean allowance?b) What is the mode of the allowances?c) Suppose two allowances of $14 and $20 are added to the list.

What is the new mean? What happens to the mode?

4. This table shows data for the Women’s National Basketball Association.a) Calculate each mean and mode:

• Games Played• Field Goals• Free Throws• Total Points

b) Who do you think is the best player? Why?

5. The graph shows the most popular sports among people older than 15 in Sportsdale.a) Which sports are equally popular?b) How could you use the bar graph

to find the mode? Explain and show your work.

c) Calculate the mean.Use estimated values from the graph.

Top 6 WNBA Scorers in 2003

Name Games Field Free TotalPlayed Goals Throws Points

Catchings 34 221 155 671

Holdsclaw 27 204 140 554

Jackson 33 254 151 698

Leslie 34 194 116 548

Smith 23 165 82 424

Thompson 28 176 81 472

Most Popular Sports among People Older Than 15

Number of People

Spo

rt

BasketballCycling

GolfHockeySkiing

SoccerSwimming

TennisVolleyball

Baseball

0 500 1000 1500 2000

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163LESSON FOCUS Use a computer to create spreadsheets.

Work with a partner.

The town library tracks the number of books people sign out.

Use AppleWorks.Follow these steps to display these data in a spreadsheet.

1. Open a new spreadsheet in AppleWorks. Click:

2. To enter the data:Click cell A1 to select it.Type: Town Library Sign Out RecordsPress Enter.

Click cell A2 to select it.Type: SeasonPress Enter.

Click cell A3 to select it.Type: WinterPress Enter.

Enter the rest of the seasons in cells A4 to A6.

Click cell B2 to select it.Type: Number of BooksPress Enter.

Click cell B3 to select it.Type the data for Winter: 1488Press Enter.

Enter the data for the rest of the seasons in cells B4 to B6.

TE

CHN O LOG

YCreating Spreadsheets Using AppleWorks

Town Library Sign Out Records

Season Number of Books

Winter 1488

Spring 1151

Summer 976

Fall 1259

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164

3. To calculate the total number of books:

Click cell A7 to select it.Type: TotalPress Enter.

Click cell B7 to select it.Type: =SUM(B3..B6)Press Enter.

You have entered the formula to find a sum.The sum of the numbers in cells B3 to B6 will be displayed.All formulas must begin with an “=” sign.

4. To calculate the mean:

Click cell A8 to select it.Type: MeanPress Enter.

Click cell B8 to select it.

Click: , then click:

Select Fixed as the Number option.

Enter 2 for Decimal Precision.

Click:The number in this cell will be displayed to the nearest hundredth.Type: =B7/4Press Enter.

You have entered a formula for division.The sum in cell B7 will be divided by 4 (the number of data).The result is the mean of the data.

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165

5. To format the spreadsheet:Click cell A1 to select it.

Click: , then click:

Click:

Repeat for cells A2, B2, A7, A8, B7, and B8.

6. Save your spreadsheet.

Click: , then click:

Name your file. Then click:

7. Print your spreadsheet.

Click: , then click:

Click:

8. Record the name of your spreadsheet.You will use it again on pages 169 and 176.

What are some advantages to using a spreadsheet?Explain.

I named my file “TownLibrary Sign Out Records.”

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L E S S O N

166 LESSON FOCUS

Drawing Bar Graphs

When you collect data it is important to make sure your data are accurate.Always make sure the numbers or measurements you collect are reasonable.Check any that seem unlikely.

166 LESSON FOCUS Draw bar graphs by hand.

You will need a measuring tape or a metre stick.Measure each other’s height.Record the heights on the board.Look at the class data. Are the results reasonable? What would make you think a result was not reasonable? Explain.Order the data for the class.Draw a bar graph to display the data.

Show and Share

Show your graph to another pair of classmates.Ask them questions about your graph.Compare your graph with your classmates’ graph.How are your graphs the same? Different?

Ms. Lindt teaches math to 25 Grade 5 students.She ordered the marks her students received from the least to the greatest.

She wants to display these data in a bar graph.

➤ There were too many pieces of data to graph each mark separately.First, she grouped the marks into equal intervals.

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167

➤ She chose the scale 1 square represents 1 student.She labelled one axis “Number of Students”and the other “Marks.”Then she drew a bar for each interval of marks and wrote a title.

I should make about 5 or 6 intervals. Each

number should belongto just one interval.

Marks of Students in Grade 5

Marks Number of Students

91–100 2

81–90 4

71–80 10

61–70 6

51–60 3

1. Which of these 3 sets of data would you group into intervals? Why? How would you group the data into intervals?Draw the bar graph for the data you grouped in intervals.a) b)

c) Masses of parcels in a mail room:27 kg, 29 kg, 30 kg, 31 kg, 31 kg, 31 kg, 32 kg, 33 kg, 34 kg,35 kg, 36 kg, 37 kg, 37 kg, 38 kg, 39 kg, 41 kg, 42 kg

Election Results Hillside Public School

Name Number of Votes

Ho 32

Kake 26

Marr 80

Neigh 30

O’Neil 24

Young 40

Number of Books ReadStudents at Flanshaw School

Number of Number of Books Students

One a week 62

One a month 72

One every 3 months 36

One every 6 months 17

One a year 13

1

Marks of Students in Grade 5

Marks

Num

ber o

f Stu

dent

s

2345678910

51–60 61–70 71–80 81–90 91–100

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2. Use the table.a) What is the range of the data?

The mean?b) Round these data to the nearest 100.

Then graph the rounded data.Which type of graph did you choose to draw? Why?

c) Which province has about double the number of police officers as British Columbia? How does your graph show this?

3. A group fitness test showed the number of curls each person could do in 1 minute:30, 45, 25, 18, 15, 35, 27, 34, 26, 32, 43, 39, 29,31, 43, 44, 26, 16, 20, 40, 44, 22, 27, 30, 36, 37a) Calculate the mean and the mode.b) Choose a suitable graph to display the data.

Explain your choice.c) Draw the graph. Show the mean on your graph.d) Which average, the mean or the mode,

is more typical of the data? Explain.

4. The students in a Grade 5 class recorded their heights in centimetres:137, 139, 139, 140, 140, 141, 142, 142, 142, 143, 144, 144,146, 147, 148, 148, 149, 150, 152, 154, 158, 159, 160a) Arrange the data into intervals.

Create a table to display the data.b) Display the data in a bar graph.c) Write 2 things you can learn

from the graph.

168 ASSESSMENT FOCUS Question 4

Grouping data into intervals makes the data moremanageable. Use an example to show why thechoice of the interval width is important.

Mental Math

Estimate each product.Which strategies did you use?

148 � 9211 � 1939 � 3298 � 102

Numbers Every Day

Number of Police Officers in 2002

Province Number of Police Officers

Nova Scotia 1 608

Quebec 14 368

Ontario 23 328

Alberta 4 999

British Columbia 7 106

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169LESSON FOCUS Use a computer to draw bar graphs and circle graphs.

Work with a partner.

Use AppleWorks.Follow these steps to graph the Town Library Sign Out data.Use the spreadsheet you created on pages 163 to 165.

1. Open a spreadsheet in AppleWorks. Click:

2. Open your Town Library spreadsheet.

Click: , then click:

Click on the name of your spreadsheet:

Click:

3. To select cells A3 to B6:Click cell A3. Hold down the mouse button.Drag the cursor from A3 to B6.Release the mouse button.

Follow Steps 4 to 6 to create a circle graph of the spreadsheet data.

TE

CHN O LOG

YDrawing Circle Graphs and Bar Graphs Using AppleWorks

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170

4. To create a circle graph:

Click: , then click:

Click the Gallery tab, click:

No options should be selected.

Give the graph a title.Click the Labels tab.Make sure Show Title and Show Legend are selected.Type: Town Library Sign Out Records

Click:

5. To move the graph:Move the cursor inside the graph box.Click and hold down the mouse button.Drag the graph below the mean.Release the mouse button.

6. To print the graph:

Click: , then click:

Click:

Follow Steps 7 to 9 to create a bar graph of the spreadsheet data.

7. To create a bar graph:

Click: , then click:

Click the Gallery tab, then click:

No options should be selected.

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171

Give the graph a title.Click the Labels tab. Select Show Title.Make sure Show Legend is not selected.Type: Town Library Sign Out Records

Label the axes.Click the Axes tab. Select X axis.Type the Axis label: Season

Select Y axis. Type the Axis label: Number of Books

Enter these settings:

Click:

8. Save your graphs. Click:

Then click:

Give your file a new name.

Then click:

9. Repeat Steps 5 and 6 to move and print your graph.

What are some advantages of graphing data using a computer?

I named my file “Circleand Bar Graphs.”

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Line Graphs

Look at this graph.

What does this graph show?How is it different from other graphs you have seen?How do the maximum temperatures in May and November compare?Which months have the same maximum temperature?Write 4 other questions you can answerfrom the graph.

Show and Share

Trade questions with another pair of classmates.Answer your classmates’ questions.How is this graph the same as a bar graph?A pictograph? How is it different?

L E S S O N

172 LESSON FOCUS Draw line graphs by hand.

Meteorologists record data regularly over time.In this lesson, you will learn to graph data to show the change in the data.

Number Strategies

Order the decimals in each set from least to greatest.

• 0.68, 0.86, 0.80• 1.35, 5.31, 5.13• 67.4, 6.74, 7.64• 2.31, 1.23, 2.13

Numbers Every Day

02

Monthly High Temperaturefor Alert Bay, BC

Month

Janu

ary

Feb

ruar

yM

arch

Apr

ilM

ayJu

neJu

lyA

ugus

tS

epte

mbe

rO

ctob

erN

ovem

ber

Dec

embe

r

Tem

pera

ture

in °C

468101214161820

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0

Population of Nova Scotia, 1950 – 1990

Year

In 1950, the populationwas 638 000.

We use a jagged lineto indicate that we arenot showing all the numbersbetween 0 and 625.

Pop

ulat

ion

(tho

usan

ds)

625

650

675

700

725

750

775

800

825

850

875

900

1950 1960 1970 1980 1990

To display these data on a line graph:

➤ Draw two axes.The horizontal axis shows time.Label the horizontal axis “Year.”The vertical axis shows the data that change over time.Label the vertical axis “Population (thousands).”

A line graph shows data points joined by line segments.

Lucy had a social studies project.She needed to show data of the population of Nova Scotia from 1950 to 1990.

173

Population of Nova Scotia

Year Population (thousands)

1950 638

1960 727

1970 782

1980 845

1990 895

If I start at 625and count by

25s, the scale willgo up to 900.

The range of the data is 257. I don’t need to show

numbers less than 625. The highest number in the

table is 895.

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➤ Choose an appropriate scale.Count by 10s for the scale on the horizontal axis.The horizontal scale is 3 squares represent 10 years.Count by 25s for the scale on the vertical axis.The vertical scale is 2 squares represent 25.

➤ Mark a point for 1950 at 638.Then mark points for the rest of the data in the same way.

➤ Use a ruler to connect each consecutive pair of points,from left to right.

➤ Give the graph a title.➤ On a line graph, when the line segments:

• go up to the right, the graph is increasing• go down to the right, the graph is decreasingThe graph goes up to the right.The population in Nova Scotia increased from 1950 to 1990.

174

You will need grid paper.

1. A survey of the population of southern sea otters is done each year.The table shows the results from 1998 to 2002.a) Draw a line graph

to display these data.b) Explain how you chose

the vertical scale.c) What happened to the number

of sea otters from 1998 to 2002?How can you tell from the graph?

0

Population of Nova Scotia, 1950 – 1990

YearP

opul

atio

n (t

hous

ands

)

625

650

675

700

725

750

775

800

825

850

875

900

1950 1960 1970 1980 1990

Year Number of Otters

1998 1955

1999 1858

2000 2053

2001 1863

2002 1846

Document1 14/7/04 10:02 AM Page 174

175ASSESSMENT FOCUS Question 3

You can display data using a line graph,a bar graph, or a pictograph. Describe a situation that best suits each type of graph. Explain your thinking.

Look through newspapers andmagazines, or on the Internet. Find a line graph. Describe the graph. What information do you get from the graph?

175

2. This table shows the growth of Rajiv’s cucumber vine.

a) Draw a line graph to display these data.b) What does the line on the graph show?c) Write 2 things you know from the graph.

3. This table shows the number of beekeepers in Ontario from 1994 to 2003. The numbers are rounded to the nearest 100.a) Draw a line graph to display these data.b) How did you choose the scale? c) What is happening to the number of

beekeepers in Ontario? How does your graph show this?

d) How many beekeepers do you think there will be in Ontario in 2004?Explain your prediction.

Year Number of Beekeepers

1994 4500

1995 4300

1996 4100

1997 4100

1998 4000

1999 3600

2000 3000

2001 3000

2003 2650

Day 1 2 3 4 5 6 7 8 9 10

Length of Vine (mm) 0 1 7 15 27 35 41 48 53 57

G5_U5 (154-191)_F1 14/7/04 10:05 AM Page 175

Work with a partner.

Use AppleWorks.Follow these steps to draw a line graph of the Town Library Sign Out data.Use the spreadsheet you created on pages 163 to 165.

1. Open a spreadsheet in AppleWorks. Click:

2. Open your Town Library spreadsheet.

Click: , then click:

Click on the name of your spreadsheet:

Click:

3. To select cells A3 to B6:Click cell A3. Hold down the mouse.Drag the cursor from A3 to B6.Release the mouse button.

4. To create a line graph:

Click: , then click:

Click the Gallery tab, then click:

No options should be selected.

Give the graph a title.Click the Labels tab. Select Show Title.Make sure Show Legend is not selected.Type: Town Library Sign Out Records

Label the axes. Click the Axes tab.Select X axis.Type the Axis label: Season

Select Y axis.Type the Axis label: Number of Books

Drawing Line Graphs Using AppleWorks

176 LESSON FOCUS Use a computer to draw line graphs.

G5_U5 (154-191)_F1 13/7/04 5:42 PM Page 176

Enter these settings:

Click:

5. To move the graph:Move the cursor inside the graph box.Click and hold down the mouse button.Drag the graph below the mean.Release the mouse button.

6. To print the graph:

Click: , then click:

Click:

7. Save your graph. Click:Then click:Give your file a new name.

Then click:

8. Look at the graph.Complete each question in your notebook.a) Describe the shape of the graph.b) Write 2 things you can tell from your graph.

9. You drew 3 different graphs to display the same data:Look at the 3 graphs.a) What can you tell from each graph that you could not tell

from the table?b) Which graph do you think displays the data the best? Why?

TE

CHN O LOG

Y

What data would be best displayed in a circle graph? A bar graph? A line graph? Explain.

177

I named my file“Line Graph.”

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L E S S O N

178 LESSON FOCUS Conduct a survey and interpret survey results.

Interpreting Survey Results

Suppose you want to find the sport 10- and 11-year-olds most like to watch.How will you do the survey?Decide on a survey question.Draw a table to record the results.Collect data for 10 people in the class.

Make up 3 questions to ask about the survey results.

Show and Share

Share your questions with another group of classmates.Ask your classmates to answer the questions.Did you ask the same survey question?Do you think the results of your survey would be the same if you surveyed 10 different people in your class?In another country? Explain.Do you think the people you surveyed represent all 10- and 11-year-olds?

Miller wants to know which candy colour is most common in a box of Gooey Chewy Candy.

Gooey Chewy Candy is sold in stores everywhere.Miller cannot check every box.So, he checks a sample of 50 boxes purchased from one store.

A sample is a small group chosen from

the entire group.

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Gooey Chewy Candy in 50 Boxes

Colour Number of Candies

Red 138Blue 16Yellow 95Orange 82Green 56White 105

179

Here are Miller’s findings:

• Miller discovered red was the most common colour of Gooey Chewy Candy.The mode colour was red.

• He calculated the mean number of candies of each colour in 50 boxes to be 82.

Miller had expected the number of each colour of candy to be about the same in each box.He thought he should sample other stores to see if their resultswere similar before concluding that there were always more redand white candies than green or blue in a box.

A sample that does not truly represent the group is biased.

1. Write a survey question for each topic.Give 4 possible answers for each question.a) favourite food b) favourite athlete c) species of pet

2. How could you conduct a school survey without questioning every student in the school? Explain how you could make sure the sample was not biased.

Math LinkYour World

Statistics Canada collects dataon many topics, such as theeconomy and the size of thepopulation. Politicians andresearchers use these data tolearn more about our countryand to make decisions.

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3. This graph shows the results of a student survey.a) Write what the survey question

might have been.b) How many students do you

think were surveyed? Explain.c) Do you think a sample or an

entire group was surveyed? Why?d) Write 2 things you know

from this survey.

4. Best Bicycle Company surveyed 10 bike stores in Ontario.It wants to find out how many of their bikes have been sold in the last 6 months. Here are the results:

a) What is happening to bike sales? Why do you think this is happening?

b) Find the mean number of bicycles sold during this period.c) Predict sales for September.

Give reasons for your prediction.

180 ASSESSMENT FOCUS Question 3

Why might you survey a sample rather thanan entire group? Explain.

Number Strategies

Round to the nearest dollar.$ 7.78$12.62$ 1.40$25.35$14.55

Numbers Every Day

05

Bicycle Sales

Month

Num

ber o

f Bik

es

10152025303540

March April May June July August

02

Computers in the Home

Location

Kitc

hen

Bedr

oom

Fam

ily ro

omNo

com

pute

r

Num

ber o

f Stu

dent

s

468101214161820

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181

Every now and then we hear about a medical breakthrough.It could be a new drug, a new treatment, or a new understandingof the human body. Often, it changes the way doctors treat aparticular illness. These advances in medicine are the result of years of research. Researchers carefully collect data, analyse and interpret the data, and present their findings.

Medical researchers conduct experiments or trials.These are tests to prove or disprove an idea.There are very strict guidelines for setting up trials.The guidelines help ensure the results are accurate.Researchers repeat experiments many times to see if they can duplicate the results. They use “control groups”or “double-blind” testing. They also have other researchers check their work. In medical research, interpreting the dataincorrectly could lead to serious damage or even death!

Medical researchers need to be careful, precise, and cautious intheir work. But a good medical researcher is also very curious andopen-minded. Researchers can’t be disappointed when they getdifferent results from those they were expecting. Even negativeresults are useful. Unexpected or strange results can sometimeslead to new discoveries. Some of the most important medicalbreakthroughs have happened “by accident.”

Medical Researcher

Wor

ld of Work

People in the controlgroup do not receivethe treatment.

In a double-blind study,neither the researcher northe participants know whois receiving the treatment.

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In the previous lesson, you learned that the data produced by a particular sample might not truly represent the entire group.Sometimes, data are displayed to suggest a particular result.

L E S S O N

Bias in Displaying Data

The points scored by 3 basketball players are shown in the table.The data are displayed in two graphs.

From the table, does there appear to be a great difference in the points each player scored?What is the range of the points?Compare Graph A and Graph B.In which graph does the range seem small?In which graph does the range seem great?How are the graphs the same? How are they different?

182 LESSON FOCUS Investigate bias in the way data are displayed.

Points Scored in a Season

Player Points

Abrams 280

Kiski 300

Snell 250

Points Scored in a Season

Players

Poi

nts

Sco

red

100

200

300

Abrams Kiski Snell240

Points Scored in a Season

Players

Poi

nts

Sco

red

250

260

270

280

290

300

Abrams Kiski Snell

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In a survey, 1000 people were asked to choose between 2 brands of shampoo.The results are displayed in two different graphs.

➤ Graphs show data in a way that is easy to see.However, graphs can also show data with bias.Bias shows data in a way that someone else wants youto see them.

➤ Look at Graph A.The difference between the numbers of people that chose Frizz Free or Shiny Locks shampoo is not very large.From Graph B, however, it appears that 3 times more people chose Frizz Free over Shiny Locks.Graph B is biased.Suppose you were advertising Frizz Free shampoo.Graph B creates the impression that Frizz Free is much more popular with customers.

Mental Math

Write 5 different number sentences with the answer 375.

Numbers Every Day

183

Show and Share

Discuss your answers with another pair of students.Discuss how the vertical scale makes the two graphs look different.Why might you choose to use Graph A? Graph B?

0

Favourite Shampoo

Brands

Num

ber o

f Peo

ple

100

200

300

400

500

600

Frizz Free Shiney Locks400

Favourite Shampoo

Brands

Num

ber o

f Peo

ple

450

500

550

Frizz Free Shiney Locks

Graph A Graph B

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Company Profit

Months

Pro

fit

$20,000

$60,000

$100,000

$140,000

10 2 3 4 5 6

Company Profit

Months

Pro

fit

$20,000

$40,000

$60,000

$80,000

$100,000

$120,000

$140,000

10 2 3 4 5 6

1. The graphs show how two students spend their allowance.

a) From the graphs, can you tell how much money Tina has? Mark has?

b) From the graphs, which student appears to spend more money on movies?

c) From the graphs, can you actually tell which student spends more money on movies? Explain.

2. A company displays its profit for 6 months on two different graphs.

a) How are the two graphs alike? How are they different?b) What were the company’s profits in month 6?c) Suppose you were writing a newsletter for the company and

wanted to emphasize profit. Which graph would you choose?Explain why.

184

How Students Spend Their Allowance

Graph A Graph B

Mark Tina

Food

MusicClothes

Movies Food

MusicClothes

Movies

Graph A Graph B

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3. In a survey, 5000 people were asked to name their favourite potato chip.The graphs show the results of a survey.

a) Look at Graph A. Does there appear to be muchdifference in the number of people who chose Krunchie over Tasty Tater or Delish?

b) Use Graph A. How many people chose Krunchie? How many chose Tasty Tater? How many chose Delish?

c) In Graph B, the bar for Krunchie is twice as high as thebars for the other brands.Can you say that twice as many people prefer Krunchie?Explain.

d) Use Graph B. How many people chose Krunchie? How many chose Tasty Tater? How many chose Delish?

e) Suppose you were advertising Krunchie.Which graph makes the range appear to be larger thanit really is? Explain.

185ASSESSMENT FOCUS Question 3

Suppose that a graph is drawn to show bias.Does this mean that the data inthe graph are incorrect? Explain.

Look through newspapersand magazines. Find anadvertisement that usesgraphs. Is there any bias?

185

Favourite Potato Chip

Brands

Num

ber o

f Peo

ple 200

100

Krunchie Tasty Tater Delish140

Favourite Potato Chip

Brands

Num

ber o

f Peo

ple

160

180

200

190

170

150

Krunchie Tasty Tater Delish

Graph A Graph B

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186 LESSON FOCUS Interpret a problem and select an appropriate strategy.

L E S S O N

Greg was playing marbles with his friends.In the first game, he lost 2 marbles.In the second game, he lost twice as many as in the first game.In the last game, he won 8 marbles.Greg finished with 25 marbles.How many marbles did he start with?

Show and Share

Describe the strategy you used to solve the problem.

Strategies

• Make a table.

• Use a model.

• Draw a diagram.

• Solve a simpler problem.

• Work backward.

• Guess and check.

• Make an organized list.

• Use a pattern.

• Draw a graph.

At school, Jasmin bought chocolate milk for $0.75,a hot dog for $1.00, and a bottle of water for $1.07.On the way home, she found a quarter on the sidewalk.At the end of the day, she had $1.37 in her wallet.How much money did Jasmin start with?

What do you know?• Jasmin finished with $1.37.• Jasmin spent $0.75, $1.00, and $1.07.• Jasmin found $0.25.

Think of a strategy to help you solve the problem.• You can work backward.• Start with $1.37.• Subtract what she found.• Add what she spent.

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187

Choose one of the

Strategies

• Subtract $0.25 from $1.37.• Add $1.07, $0.75, and $1.00.• How much money did Jasmin start with?

How can you check your answer?How could you have solved this problemanother way?

1. On Saturday Jo walked her dog for 20 minutes more than she did on Sunday. For both days she walked a total of 1 hour 15 minutes.For how long did Jo walk her dog on Saturday?

2. All 5 students in Carlo’s group saved some money eachweek toward the cost of a trip. The mean amount ofmoney saved one week by the group was $2.50.Suppose each student saved a different amount.How much might each have saved that week?

3. Ari lines up his hockey cards with the same number ofcards in each row. The card in the middle of the array has 5 cards above, below, to the right, and to the left.How many cards does Ari have?

How can working backward help you solve a problem? Use words and numbers to explain.

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188

Show What You Know

1

23

LESSON

Ontario's Sources of Electricity in 2003

Oil&Gas

Nuclear

Hydroelectric

Coal

Other

Name Games Played

Allen 76

Bryant 82

Duncan 81

Garnett 82

Iverson 82

McGrady 75

Nowitzki 80

O’Neal 67

Pierce 79

Webber 67

1. This graph shows the sources of Ontario’s electricity in 2003.a) Which sources each provide most of

Ontario’s electricity? How does the graph show this?

b) Which sources each provide less than �14� of

Ontario’s electricity?c) About what fraction of Ontario’s electricity

comes from oil and gas?

2. Here are the masses, to the nearest kilogram,of a group of Grade 5 students:26, 28, 30, 32, 32, 32, 33, 33, 34, 35, 35, 36, 37,37, 37, 37, 38, 38, 39, 39, 40, 41, 42, 43, 43 a) What is the mean mass?b) Arrange the data into intervals.

How did you decide on the intervals? c) Display the data in a bar graph.d) Write 3 questions you can answer using the graph.e) Answer your questions.

3. This table shows the number of gamesthe top 10 National Basketball Asssociation scorers played in 2003.a) Find the mean number

of games played.b) Find the mode.c) Find the range of

the data.d) Display these data

in a graph.

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interpret and evaluate data intables and graphsdraw labelled graphs by handand with a computerrecognize accuracy or bias intables and graphsexamine how data werecollected and if they arereasonablefind the mean and the modeof a set of datapredict the results of a surveydesign and conduct a survey

Learning GoalsU N I T

LESSON

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56

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189

Year Amount

1999 $19

2000 $22

2001 $17

2002 $16

0

Favourite Candy

Type of Candy

Num

ber o

f Peo

ple

25

50

75

100

125

150

Chewy Hard90

Favourite Candy

Type of Candy

Num

ber o

f Peo

ple

100

110

120

130

140

150

Chewy Hard

4. A survey of Canadians aged 9 to 14 was conducted.The table shows how many dollars each spend on music CDs for every $100 they spend.a) Draw a line graph to show these data.b) Describe the graph.c) What do you think the data will be for 2003? Explain.

5. These graphs show how many people prefer each type of candy.

a) How are the two graphs similar? How are they different?

b) Which graph shows bias? Explain why.

6. Conduct a class survey about favourite hockey teams.a) Write the question you will ask.b) Conduct the survey.c) Display the results.d) Write about your survey.

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190

In the Lab

When scientists conduct experiments they collect and study data.You will conduct an experiment to collect and study data.

Part 1

Work in a group.Decide on a question that may be answered by doing an experiment.Design the experiment.What do you expect the results might be?

Part 2

Conduct the experiment.Remember to:• Write down what you want to find out.• List each step of the experiment.• List any materials you need.• Record your data in a table.• Draw and label a graph to display your data.• Write the results of the experiment.

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Check List

191

Part 3

Trade results with another group.Check each other’s work.Are the results reasonable? Discuss why or why not.

Part 4

Present your results to the class.Discuss what you learned from your experiment.

Describe some ways you can display data.When would you use each way?Use examples to explain.

Your work should show that you created a plan to answer your experiment question how you collected andrecorded data accuratelya graph that is easy tounderstand, with labels and titlea clear explanation of your results

✓

✓

✓

✓

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