Having completed this chapter, you are now able to:
• determine the types of graphs that can be used to represent a given data set, and explain the advantages and disadvantages of each;
• create, with and without technology, a graph to represent a given data set;
• describe the trends a graph represents for a given data set;
• interpolate and extrapolate values from a given graph;
• explain how the same graph can be used to justify more than one conclusion;
• explain how different graphic representations of the same data set can be used to emphasize a point of view;
• solve contextual problems that involve the interpretation of graphs; and
• critically analyze data presented graphically to determine accuracy and reliability.
You will also have finished a chapter project that allowed you to use your graphing skills in a realistic workplace context.
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praCtIse your neW skIlls
1. Mango rice pudding and spicy dumpling soup are some of the foods made at Chiang’s Cafe in downtown Regina. Mei is the head cook at the café. Her manager has asked Mei to tell him how much money is lost each month due to food waste, so that Mei will know when to order fewer perishable supplies such as fresh
vegetables and dairy products. Mei must record the amount and type of food waste, and then calculate and record its cost. Display Mei’s information on a suitable graph.
food Waste
Month J F M A M J J A S O N D
Cost of food
waste $135.00 $125.00 $92.00 $53.00 $86.00 $72.00 $97.00 $89.00 $112.00 $98.00 $82.00 $47.00
2. Wilhelmina found the following graph while she was doing a research project.
s
830 892 954 1016 1078 1140
Oct. 09Jul. 09
Apr. 09Jan. 09
Oct. 08Jul. 08
Apr. 08Jan. 08
Oct. 07
m National Salary Trends For Electricians
Salary ($)
Month
a) What does the graph seem to indicate?
b) In what way is the graph misleading?
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3. In his beauty salon, Gus sells eight different colours of nail polish. He used the following broken line graph to display the number of people who chose each colour. Number of Each Colour
Chosen by Clients
a) Was this the most suitable way to display the data?
Explain your answer.
b) Identify and justify another type of graph that could have been used and display the data on that graph.
4. Canada is known to be a multicultural/multilingual
country. Thus, Canadians have many different first languages. A recent census recorded the following mother tongues of Canadians and the number of people who spoke them (in thousands).
soMe CanadIan languages
Language Number (1000s) Language Number (1000s)
English 17 883 French 6817
Cantonese 361 Mandarin 171
Hakka 4 Chinese (other) 457
Italian 455 German 451
Polish 211 Spanish 345
Portuguese 219 Punjabi 368
Ukrainian 135 Arabic 262
Dutch 129 Tagalog 236
Greek 117 Vietnamese 142
Cree 79 Inuktitut 32
Other 1956
a) Choose a suitable type of graph on which to display the data and draw the graph.
b) Think of a second type of graph you could have used to display the data. Explain any advantages or disadvantages of one over the other.
hInt
A graphing program may make it easier to convert from one graph to another.
Currently, the largest number of new Canadian immigrants come from China and South Asia.
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5. Census takers for Statistics Canada listed the population of Canada (in thousands of people) on July 1, 2009 as 33 739.9. The following table indicates the population by province and territory from this census.
Canada's populatIon
Province NL PE NS NB QC ON MB SK AB BC YT NT NU
Population 508.9 141.0 938.2 749.5 7828.9 13 069.2 1222.0 1030.1 3687.7 4455.2 33.7 43.4 32.2
a) Represent the population by province and territory as a horizontal bar graph by number of people.
b) Represent the population by province and territory as a circle graph by percent of population.
c) Discuss which graph seems to give a better view of the population distribution.
6. Harpinder is a plumber who specializes in small household repairs. He keeps an inventory of some basic stock in his truck so that he can usually repair the plumbing without returning to his store. This saves him a lot of time so that he can make more visits each day. Last week he made the following numbers of house calls: Monday, 5; Tuesday, 3; Wednesday 7;
Thursday, 5; Friday, 2.
a) Represent the information on a graph.
b) Explain why you chose this type of graph.
c) Could you have represented the data with a different graph, and if so, what kind?
7. While considering the job market for electricians, Jody found the graph to the right depicting average incomes for different types of electricians.
0
Type of Electrician
Average Annual Electrician Salaries
a) Which type of electrician has the highest average salary? Approximately how much does he or she make a year?
b) High voltage, aircraft, commercial, and senior electricians earn approximately the same amount. How much is this a year?
c) Could this information have been presented on a different type of graph? Explain why or why not for each of the other three graph types.
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8. While working in the forestry industry, Ray had to determine the number of trees at each height in a given area. He displayed the information on the following chart.
0
Number of Trees of Each Height
Number of Trees
Height of Trees (ft) a) Discuss the suitability of this type
of graph for displaying the data.
b) According to this chart, what is the height of the tallest tree in the area?
c) How many trees are 50 feet tall or more?
d) How many trees are shorter than 50 feet?
e) Could the information have been displayed effectively on a different type of graph and, if so, what type?
9. Louise has indicated that she has 45% of her farmland seeded in wheat, 20% in oats, 15% in canola, and the rest is summer fallow. Display this data on a suitable graph and justify your choice. Are there any alternative graphs that could be used? List them, and explain why.
10. For the following data, low wage refers to the hourly wage of the bottom 10% of the workers in the field, and high wage refers to the hourly wage of the top 10% of workers in the field.
hourly Wages In Calgary
Job Low wage Average wage High wage
Electrician $29.00 $30.00 $37.00
Plumber $15.00 $21.00 $30.00
Carpenter $12.00 $30.00 $35.00
Painter and decorator $12.00 $19.00 $32.00
Truck driver $14.00 $20.00 $30.00
Cable worker $14.00 $22.00 $45.00
Crops grown in Canada include flaxseed, durum wheat, and canary seed.
Canada leads worldwide production of canary seed, which comes from the canary grass plant and is used in birdseed mixes.
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a) Make a triple bar graph to compare the low, average, and high wages for workers in Calgary.
b) Which occupation has the greatest discrepancy in wages?
c) Which occupation has the least discrepancy in wages?
d) Discuss how you can use the average wage in comparison to the highest and the lowest to determine if more people are in the upper or lower wage category.
11. Similar figures are available for workers in Winnipeg.
hourly Wages In WInnIpeg
Job Low wage Average wage High wage
Electrician $14.00 $24.00 $28.00
Plumber $14.00 $20.00 $29.00
Carpenter $15.00 $30.00 $35.00
Painter and decorator $9.00 $16.00 $25.00
Truck driver $13.00 $20.00 $33.00
Cable worker $11.00 $17.00 $25.00
a) Using the same scale as for the previous question, draw a triple bar graph to represent this data.
b) Are the highest and lowest paid occupations the same in both cities?
Justify your response.
c) Compare the Calgary graph to the Winnipeg graph. Discuss any general trends or patterns you see.
d) On average, a carpenter in Calgary makes $10.00 an hour more than a carpenter in Winnipeg. If you were a carpenter free to move to either city, what considerations other than average wage could be important?
12. Using the data from the previous two questions, make at least one graph that compares the salaries between the two cities.
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Chapter 3 Surface Area, Volume, and Capacity
goals
Many of the objects that you see every day are common three-dimensional objects. The soccer ball you played with is a sphere, the ice cream cone you ate is a cone, and the cereal box that holds your breakfast is a rectangular prism. When your soccer ball was created, someone measured how much leather would be needed to cover the ball. When your cereal box was designed, someone measured the space inside to determine how much cereal it could hold.
In this chapter, you will
• estimate and calculate the surface area of a three-dimensional object;
• estimate, measure, and calculate the volume of a three-dimensional object;
• modify your surface area and volume measurements when their dimensions increase or decrease; and
• explore the relationships between several objects and determine how their volumes are related.
key terMs
• cone
• cylinder
• dimension
• prism
• pyramid
• sphere
• surface area
• volume
• capacity
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PRojeCt—DeSIGnInG PACKAGeS start to plan
projeCt overvIeW
Good packaging promotes a product through interesting design while protecting it with practical design features. It should be colourful, eye-catching, and tailored to the object it contains.
Packaging is designed to attract customer attention and protect the product inside.
In this project, it will be your job to give a product visual punch. You will take on the role of a packaging designer who must create three different packages for the same item.
You will propose three different packages to the executive team of your company, along with the associated costs for each package. To do this:
• each package must have a different shape (for example, you cannot design three boxes of the same shape and size);
• one package should incorporate two shapes (for example, a box with a domed lid).
get started
Your packaging can be designed for an item of any size and price. It can be as small as a ring or as large as a car. Think of an item you would like to buy and something you would enjoy promoting, as well as how you would package it.
Three-dimensional packages are usually in the shape of a rectangular prism, but you needn’t limit yourself to this shape. Think of wedge-shaped boxes for individual pizza slices, curvy cylindrical beverage bottles, or semi-spherical containers for headphones.
List and answer the different choices you will need to make to design your packaging. For example:
• What shapes will your packages be?
• How can you combine different shapes into your packaging?
• How can you design your packaging to fit, contain, and protect your item?
• How will you calculate the surface area, height, width, length, and volume of your different packages?
• Which unit will you use to measure these variables?
fInal presentatIon CheCklIst
Your final project and presentation will contain the following information:
• a drawing of your item and three packages;
• the associated dimensions and three-dimensional measurements for each package;
• your research on package dimensions, your customer, and the materials commonly used to build your package;
• the cost to create each package; and
• a poster, handout, or electronic presentation.