Graphical representations of data Block 1 Student Activity ... · Graphical representations of data Block 2 Student Activity Sheet 9. REINFORCE Think about ten questions that would

Student: Class: Date:

Graphical representations of data Block 1 Student Activity Sheet

1. A statistical question is one that expects a variety of answers. Here are some examplesand non-examples. Add two more of your own to each column.

Statistical questions Not statistical questions How old are your family members? How old are you? What is the cost to adopt a dog at this rescue?

What is the cost of adopting the poodle with the red collar?

What are the most popular dog breeds? What is Maria’s favorite breed of dog?

2. Maria has a lot of data that were presented using different graphs. What questions mightMaria have asked after looking at the three graphs?

3. What questions would you ask if you were choosing a dog for your family? Write themdown. Later, once you look at other data that might help you answer the questions, youcan determine whether they are resolved in a satisfying way.

Copyright 2015 Agile Mind, Inc. Content copyright 2015 Charles A. Dana Center, The University of Texas at Austin

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4. REINFORCE In the table are questions for a group of 20 middle school students. For each

question, determine whether it is a statistical question. Then explain why or why not.

Question Is it a statistical question?

Why or why not?

What is your favorite flavor of ice cream?

Yes There are lots of different flavors of ice cream and not everyone has the same favorite.

a. How long did it take you to get to school today?

b. Who is the principal of our school?

c. Who is your math teacher?

d. How many siblings do you have?

e. What color shirt did you wear yesterday?





1. Suppose you asked a question to 15 people: "Of the Golden Retriever, Poodle, Labrador,

Maltese, and Chihuahua dog breeds, which is your favorite?" How do your results change if you ask, "If you could choose from all the breeds of dogs in the world, what is your favorite?"

Which kinds of questions ask for numerical data and which ask for categorical? Fill in each blank with the word categorical or numerical, based on the type of information the question could provide. 2. How tall are you?

3. What is your favorite color?

4. What restaurant makes the best burgers?

5. How many calories are in your favorite burger?

6. How many pets do you own?

7. What is your age?

8. What kind of pet do you own?





9. REINFORCE Think about ten questions that would help your family make a good decision

about choosing a dog. Then for each, decide how you would find the answer to the question and whether the data is categorical or numerical.

Question How to Find the Answer Categorical

or Numerical

1

2

3

4

5

6

7

8

9

10 After looking at the information given to her at the adoption center, Maria decided she needed to learn more about dog breeds. What data might she have gathered to answer the questions below?

10. What kinds of dogs are most popular? 11. How big do they get?





12. What is the cost of adoption? 13. How long do they live? 14. Maria received a table from the American Kennel Club (AKC) showing data from the top

20 dog breeds. Do the data in the table help to answer any of the questions you've been thinking about? Which data helped you answer each of your questions?





American Kennel Club Top 20 Breeds 2004

Breed Type Of breed

Number of dogs

Registered 2004

Height Female (in cm)

Height Male

(in cm)

Weight Female (in lbs)

Weight Male

(in lbs)

Life Expectancy (in years)

Average Price

Beagle Hound 44,555 33-38 36-41 20-23 22-25 12-15 $700 Boston Terrier

Non-sporting 16,464 38.1-43 38.1-43 10-25 10-25 15 $797

Boxer Working 37,741 53-61 56-63 53-65 60-70 11-14 $1,074

Bulldog Non-sporting 19,396 31-40 31-40 49-51 53-55 8 $800

Chihuahua Non-sporting 24,850 15-23 15-23 2-6 2-6 15 or more $742

Dachshund Hound 40,770 35-45 35-45 9 9 12-15 $770 German Shepherd Herding 46,046 55-60 60-65 77-85 77-85 13 $718

Golden Retriever Sporting 52,550 51-56 56-61 55-70 60-80 10-12 $667

Labrador Retriever Sporting 146,692 53-58 56-61 55-70 60-75 10-12 $603

Maltese Toy 13,683 20-23 21-25 6 1/2-9 6 1/2-9 15-18 $1,100 Miniature Schnauzer Terrier 24,080 30-36 30-36 10-15 10-15 15 $664

Pointer (German Shorthaired)

Sporting 12,799 53-58 59-64 45-60 55-70 12-15 $625

Pomeranian Toy 21,269 18-30 28-38 3-7 3-7 15 $854

Poodle Non-sporting 32,671 28-38 18-30 15-17 15-17 12-15 $790

Pug Toy 23,152 25-30 30-36 13-18 13-20 12-15 $1,012

Rottweiler Working 17,498 56-63 61-69 85-115 95-130 10-12 $500 Shetland Sheepdog Herding 15,605 30-36 33-38 12-16 14-18 12-15 $553

Shih Tzu Toy 28,958 Up to 28

Up to 28 9-16 9-16 15 or more $800

Cocker Spaniel Sporting 18,553 36.8 38 15-30 15-30 12-15 $559

Yorkshire Terrier Toy 43,522 15-17.5 15-17.5 7 7 12-15 $600





The following data are provided for use with the Guided practice.

Crème de la Crème Data Name of product Type of

Flavor Total

Calories Calories from

Fat Vitamin A (% of RDA)

Calcium (% of RDA)

Ice Cream Amaretto Ice Cream Other 390 210 20 20 Banana Ice Cream Fruit 370 200 15 20

Black Cherry Ice Cream Fruit 390 200 15 20 Butter Pecan Ice Cream Nut 390 210 20 20 Cake Batter Ice Cream Other 410 200 15 20 Candy Cane Ice Cream Candy 420 210 15 20

Caramel Ice Cream Other 390 210 20 20 Cheesecake Ice Cream Other 390 200 15 20 Chocolate Ice Cream Other 390 210 15 20 Cinnamon Ice Cream Other 400 210 20 25

Coffee Ice Cream Other 400 210 20 20 Cotton Candy Ice Cream Candy 390 210 20 20

Egg Nog Ice Cream Other 400 200 15 20 French Vanilla Ice Cream Other 400 200 20 20

Irish Cream Ice Cream Other 390 210 20 20 Macadamia Nut Ice Cream Nut 390 210 20 20

Mango Ice Cream Fruit 370 200 25 20 Mint Ice Cream Other 400 200 15 20

Mocha Ice Cream Other 390 210 15 20 Orange Dreams Ice Cream Fruit 370 200 15 20

Peach Ice Cream Fruit 380 200 25 20 Peanut Butter Ice Cream Nut 440 260 15 20 Pecan Praline Ice Cream Nut 390 200 15 20

Pistachio Ice Cream Nut 390 210 20 20 Raspberry Ice Cream Fruit 390 200 20 20

Sinless Sans Fat Sweet Cream Other 180 0 35 4

Strawberry Ice Cream Fruit 380 200 15 20

Sweet Cream Ice Cream Other 390 210 20 20

Vanilla Bean Ice Cream Other 400 210 15 20

White Chocolate Ice Cream Other 390 210 20 20





Non-Fat and Low-Fat Frozen Yogurt

Sweet Cream - Non-Fat Other 220 0 35 4

Cheesecake - Non-Fat Other 230 0 30 4

Chocolate - Low-Fat Other 230 15 35 4

Coffee - Non-Fat Other 220 0 35 4

Sherbet

Lemon Sherbet Fruit 180 0 0 4

Raspberry Sherbet Fruit 200 0 0 20

Tangerine Sherbet Fruit 200 0 0 70





1. Consider the circle graph Maria saw on a poster at the Companions Pet Rescue.

a. What information can you interpret from this graph of the dogs in the adoption center?

b. Using the circle graph, what can you say about the golden retrievers?





2. Study the different sections of the circle graph and connect them with each breed of

dog. Compare the size of each section to that of the other sections. Estimate the percentage of each section in the circle. Then decide which of the following statements are TRUE and which are FALSE.

Poodles make up more than half the dogs in the adoption center.

Labradors make up a bit more than 25% of the dogs in the adoption center.

The number of Maltese dogs is less than the number of poodles.

Labradors and golden retrievers together make up about 75% of the dogs in the adoption

center.

The number of Maltese plus “other” dogs is greater than the number of Labradors.

3. Study the table and record the number of the breeds of dogs that belong in the small, medium, and large categories.

Small

(under 10 lbs.) Medium

(between 10 and 30 lbs.) Large

(over 30 lbs.)





American Kennel Club Top 20 Breeds 2004.

Breed Type Of breed

Number of dogs

Registered 2004

Height Female

(in centimeters)

Height Male (in

centimeters)

Weight Female

(in pounds)

Weight Male (in

pounds)

Life Expectancy (in years)

Average Price

Beagle Hound 44,555 33-38 36-41 20-23 22-25 12-15 $700 Boston Terrier Non-

sporting 16,464 38.1-43 38.1-43 10-25 10-25 15 $797

Boxer Working 37,741 53-61 56-63 53-65 60-70 11-14 $1,074 Bulldog Non-

sporting 19,396 31-40 31-40 49-51 53-55 8 $800

Chihuahua Non-sporting

24,850 15-23 15-23 2-6 2-6 15 or more $742

Dachshund Hound 40,770 35-45 35-45 9 9 12-15 $770 German Shepherd Herding 46,046 55-60 60-65 77-85 77-85 13 $718 Golden Retriever Sporting 52,550 51-56 56-61 55-70 60-80 10-12 $667

Labrador Retriever Sporting 146,692 53-58 56-61 55-70 60-75 10-12 $603 Maltese Toy 13,683 20-23 21-25 6 1/2-9 61/2-9 15-18 $1,100

Miniature Schnauzer

Terrier 24,080 30-36 30-36 10-15 10-15 15 $664

Pointer (German Shorthaired)

Sporting 12,799 53-58 59-64 45-60 55-70 12-15 $625

Pomeranian Toy 21,269 18-30 28-38 3-7 3-7 15 $854 Poodle Non-

sporting 32,671 28-38 18-30 15-17 15-17 12-15 $790

Pug Toy 23,152 25-30 30-36 13-18 13-20 12-15 $1,012 Rottweiler Working 17,498 56-63 61-69 85-115 95-130 10-12 $500

Shetland Sheepdog Herding 15,605 30-36 33-38 12-16 14-18 12-15 $553 Shih Tzu Toy 28,958 Up to 28 Up to 28 9-16 9-16 15 or more $800

Cocker Spaniel Sporting 18,553 36.8 38 15-30 15-30 12-15 $559 Yorkshire Terrier Toy 43,522 15-17.5 15-17.5 7 7 12-15 $600

Source: AKC, www.akc.org, 2006 Use the data from the American Kennel Club about the most popular dog breeds in 2004 to answer this question.





4. What is the fraction of the 20 most popular dogs that represents the number of small-breed dogs?

5. What is the fraction of the 20 most popular dogs that represents the number of medium-breed dogs?

6. What is the fraction of the 20 most popular dogs that represents the number of large-breed dogs?

7. Fill in the equivalent fractions and the resulting percents.

8. Study the table. What can you say about the relative frequencies of the three categoriesof dog sizes?

Category Frequency Relative Frequency Small 6 30%

Medium 7 35% Large 7 35% Total 20 100%





Copyright 2015 Agile Mind, Inc. ® Content copyright 2015 Charles A. Dana Center, The University of Texas at Austin


1. Use the table of small, medium, and large dogs to draw the sections of the circle graphrepresenting the three size categories of dogs. Choose a color for each category.

2. Shade the percent bar graph to represent the relative frequencies of the dog sizes.Remember to label each section with its category and percent.





3. The relative frequency table, circle graph, and percent bar graph all contain the sameinformation. The representations all show the percentage of dog breeds in each sizecategory.

a. What do the representations tell you about the distribution of dog breeds among the three size categories?

b. Can you see this information equally well from the three representations?





4. Complete the following statements to describe the best representations to use indifferent situations involving categorical data.

bar graph with

frequencies

percent bar

graph

circle graph with

percents

circle graph with

frequencies

relative frequency

table

When you want to know the total number in all of the categories, use a

or . When

you want to compare a part to the whole, use a ,

a , or a .





1. What do you think is different about the bars on a histogram, compared to the bars on a bar graph?

2. Create a stem-and-leaf plot from the 25 heights Stella collected, listed below.





3. Study the stem-and-leaf plot you just created. You will be using these data to create ahistogram.

a. What are some things you notice about the shape of the data?

b. Which bar of the histogram do you predict will be the tallest?

c. Which measurements will you use in deciding how much of the number line will formthe horizontal axis of the histogram?

4. Create a histogram from the stem-and-leaf plot of the puppy measurement data.





5. What if Stella added a dog height of 40 cm to the data set? Which bar would that valuego in? Why?

Use the graph to answer questions 6 and 7. REINFORCE

6. Create a relative frequency table showing the percent for each category. Show theprocess you used to determine the percentage.Type of Flavor Relative frequency (%)

a. Fruitb. Nutc. Candyd. Other





7. How can you use the percentage of fruit flavors to find the percentage for nuts and theother flavor categories?





1. What if Stella and her friends measured 250 puppies? What hints would you give her toorganize all 250 measurements?

2. Using the interval information for 250 puppies, draw the histogram.





3. Each description below is a step to create a histogram. There are 8 steps, but right nowthey are out of order. Order the steps by placing a number (1-8) in front of each step.

Draw bars up to the appropriate height (frequency) on the vertical axis. The bars must touch one another and be of equal width. Find the difference between the largest and smallest values of the entire dataset. (This is the range for the entire data set.)

Determine the beginning and ending value for each interval. (The intervals must have equal “width.”) Choose the number of intervals for your histogram. (5 to 10 intervals is best.)

Sort the data into each interval.

On the horizontal axis write the interval values and an appropriate label.

On the vertical axis write the frequencies and an appropriate label.

Organize the data using a stem-and-leaf plot or other type of organizational tool.

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Graphical representations of data Block 1 Student Activity ... · Graphical representations of data Block 2 Student Activity Sheet 9. REINFORCE Think about ten questions that would