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Algebra 1 Copyright © Big Ideas Learning, LLC Resources by Chapter All rights reserved. 386

Chapter 11 Family and Community Involvement (English) .......................................... 387

Family and Community Involvement (Spanish) ......................................... 388

Section 11.1 ................................................................................................. 389

Section 11.2 ................................................................................................. 394

Section 11.3 ................................................................................................. 399

Section 11.4 ................................................................................................. 404

Section 11.5 ................................................................................................. 409

Cumulative Review ..................................................................................... 414

Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. Resources by Chapter

387

Chapter

11 Data Analysis and Displays

Name _________________________________________________________ Date __________

Dear Family,

In this chapter, your student will learn how data is analyzed and displayed. One career that utilizes many of the concepts discussed in this chapter is a statistician. A statistician's job is not only to collect the data, but also to analyze the data in regards to a specific setting to draw conclusions from that data. Using the Internet, research some of the different fields a statistician may work in.

• List 4 to 5 different fields a statistician may work in.

• What type of data do statisticians collect?

• Why would a company hire a statistician? Explain your reasoning.

Consider basketball.

• What kind of data would be important for a team to have analyzed?

• How would this data be beneficial in acquiring or trading players?

• Does the team statistician use measures of central tendency to represent the data from a game?

• What types of data displays would be beneficial for the coaches to see following a game?

How about other sports? Would a team from a different sport use similar methods to collect information about its athletes?

Finally, do some research on either a favorite sports team or a specific athlete.

• What type of “stats” are collected?

• Interpret the stats. What do they tell you about the team or athlete?

• Compare stats from previous years to the current year. How have the stats changed over the years? Was there improvement?

• Compare the stats from another team or player to the team or player you chose. How do they compare? How do you know which is better?

The field of sports is only one of many areas in which statistics are used. Collecting and analyzing data is found in a wide variety of other careers as well. Spend time as a family exploring how statistics is used in these careers.


Capítulo

11 Análisis y representaciones de datos

Nombre _______________________________________________________ Fecha ________

Estimada familia: En este capítulo, su hijo aprenderá cómo se analizan y representan los datos. Un profesional que utiliza muchos de los conceptos que se comentan en este capítulo es un estadístico. El trabajo de un estadístico no sólo implica recopilar datos, sino también analizar los datos con respecto a una situación específica para sacar conclusiones a partir de esos datos. Usen Internet para investigar algunos de los diferentes campos en los que puede trabajar un estadístico.

• Enumeren 4 o 5 campos diferentes en los que puede trabajar un estadístico. • ¿Qué clase de datos reúnen las estadísticos? • ¿Por qué una compañía contrataría a un estadístico? Expliquen su

razonamiento. Consideren el básquetbol.

• ¿Qué clase de datos serían importantes para analizar un equipo? • ¿Cómo serían beneficiosos estos datos para comprar o intercambiar

jugadores? • ¿El estadístico del equipo usa medidas de tendencia central para

representar los datos de un partido? • ¿Qué clases de representaciones de datos serían beneficiosas que los

entrenadores vean después de un partido? ¿Qué sucede en otros deportes? ¿Un equipo de otro deporte usaría métodos similares para reunir información sobre sus atletas? Por último, investiguen ya sea un deporte favorito o un atleta específico.

• ¿Qué clase de "estadísticas" se recopilan? • Interpreten las estadísticas. ¿Qué le indican sobre el equipo o el atleta? • Comparen las estadísticas de los años anteriores con las de este año.

¿Cómo han cambiado las estadísticas con el transcurso de los años? ¿Hubo alguna mejora?

• Comparen las estadísticas de otro equipo o jugador con el equipo o jugador que eligieron. ¿Cómo se comparan? ¿Cómo saben cuál es mejor?

El campo de los deportes es solo una de las muchas áreas donde se usan las estadísticas. La recopilación y el análisis de datos también se encuentran en una amplia variedad de profesiones. En familia, dediquen un rato a explorar cómo se usan las estadísticas en estas profesiones.


389

11.1 Start Thinking

Using a printout from your teacher, obtain a list of your percentages on tests in your math class for the current school year. Arrange the percentages from least to greatest.

What was your lowest percentage on a test? your highest? What is the difference between the two? Which percentage did you achieve the most often (if any)? What percentage is in the middle?

Divide. Round to the nearest tenth, if necessary.

1. ( )13 7÷ − 2. ( )55 7− ÷ 3. 486

−

4. 866−

5. ( )1 10÷ − 6. ( )20 1− ÷ −

7. ( )19 4÷ − 8. ( )143 11− ÷ 9. 444

−

Find the vertex and the axis of symmetry of the graph of the function.

1. ( ) 24f x x= 2. ( )219 3y x= − +

3. ( ) ( )23 2g x x= − 4. ( ) ( )215 9r x x= −

5. ( ) ( )216 4d x x= + 6. ( ) ( )21

5 5f x x= +

11.1 Warm Up

11.1 Cumulative Review Warm Up


11.1 Practice A

Name _________________________________________________________ Date _________

In Exercises 1 and 2, (a) find the mean, median, and mode of the data set and (b) determine which measure of center best represents the data. Explain.

1. 3, 5, 2, 4, 3, 4, 3, 5, 16 2. 13, 16, 10, 15, 12

3. The table shows the lengths of 9 songs.

a. Find the mean, median, and mode of the lengths.

b. Which measure of center best represents the data? Explain.

c. Identify the outlier. How does the outlier affect the mean, median, and mode?

d. Describe one possible explanation for the outlier.

In Exercises 4 and 5, find the value of x.

4. 3, 6, 4, 10, ;x The mean is 6. 5. 13, 15, 17, , 20, 21;x The median is 18.

6. The heights of a boys and girls track team are shown. Find the range of the heights for each team. Compare your results.

In Exercises 7 and 8, find (a) the range and (b) the standard deviation of the data set.

7. 15, 25, 10, 20, 35 8. 110, 88, 92, 104, 113, 107

9. Consider the data in Exercise 6.

a. Find the standard deviation of the heights of the boys track team. Interpret your result.

b. Find the standard deviation of the heights of the girls track team. Interpret your result.

c. Compare the standard deviations for the boys and the girls track teams. What can you conclude?

Song lengths (minutes) 3.2 3.5 3.2 3.8 7.2 4.2 3.4 3.5 3.5

Boys’ heights (inches) 84 75 77 82 80 80 81 78 79 80

Girls’ heights (inches) 70 66 68 72 75 70 67 70 72 67


391

11.1 Practice B

Name _________________________________________________________ Date __________

In Exercises 1 and 2, (a) find the mean, median, and mode of the data set and (b) determine which measure of center best represents the data. Explain.

1. 5, 9, 4, 2, 5, 6, 7, 5, 9, 1, 9, 4 2. 24, 18, 4, 20, 22, 26, 22, 24

3. The table shows the weights of hams (in pounds).

a. Find the mean, median, and mode of the lengths.

b. Which measure of center best represents the data? Explain.

c. A tenth ham is added, which weighs 6.5 pounds. How does this additional value affect the mean, median, and mode? Explain.

In Exercises 4 and 5, find the value of x.

4. 11.5, 12, 14.5, ;x− − The mean is 0.5. 5. 42, 55, , 80;x The median is 66.

6. The table shows the lengths of hospital stays (in days) of patients due to gastrointestinal blockage.

a. Identify the outlier. How does the outlier affect the mean, median, and mode?

b. Describe one possible explanation for the outlier.

In Exercises 7 and 8, find (a) the range and (b) the standard deviation of the data set.

7. 74, 52, 65, 64, 58 8. 11.0, 8.8, 9.2, 10.4, 11.5, 12.7

9. Find the values of the measures shown when each value in the data set is multiplied by 3.

Mean: 180 Median: 175 Mode: 150

Range: 80 Standard deviation: 24.5

Ham weight (pounds) 9.35 6.72 10.12 9.51 8.89 7.5 10.8 7.1 9.45

Length of stay (days) 3 2 2 3 4 20 3 2 4


11.1 Enrichment and Extension

Name _________________________________________________________ Date _________

Challenge: Measures of Central Tendency In Exercises 1–4, create your own real-life problems that will result in the following solutions. You must use a sample size of 10.

1. The mean of your data set is 13.5, and the mode is 10.

2. The mode of your data set is 25, and the range is 8.

3. The median of your data set is 67, and the mean is 60.

4. The mean and the median of your data set are the same.

Complete the exercise using your knowledge of measures of central tendency.

5. You and your family live in Northwestern Florida. The Farmers Almanac is predicting an unseasonable amount of rain for the year 2014. You and your siblings decide to keep track of the number of rainy days each month. The data you collect are as follows: 10, 11, 11, 14, 12, 10, 13, 7, 15, 11, 13, 14.

a. Find the mean, median, mode, and range of your data.

b. If the number of days it rains each month gets cut in half in the year 2015, what would be the mean, median, mode, and range?

c. If, instead, there were three fewer rainy days each month in the year 2015, what would the mean, median, mode, and range be?


393

Puzzle Time

Name _________________________________________________________ Date __________

How Do You Stop A Skunk From Smelling? Write the letter of each answer in the box containing the exercise number.

Find the mean, median, and mode of the data set.

1. 4, 4, 2, 7, 1, 2, 3, 4, 18

2. 14, 7, 19, 13, 12

3. 8, 35, 12, 23, 16, 26, 21, 35

Find the value of x.

4. 6, 4, 13, 3, 10, ;x The mean is 10.

5. 11, 12, 14, , 22, 27;x The median is 16.

6. 14.5, 8, 4.5, ;x− − The mean is 9.5.

7. 40, 55, , 110;x The median is 61.

Find the range and the standard deviation of the data set. 8. 20, 15, 25, 35, 40

9. 43, 17, 19, 37, 38, 20

10. 8.1, 12.2, 1.5, 5.9, 2.3, 6.7, 9.1, 2.2

11. Find the values of the measures shown when each value in the data set increases by 12.

Mean: 40 Median: 36 Mode: 36

Answers

I. 18

P. 67

U. 24

N. 36

S. mean: 22; median: 22; mode: 35

O. range: 10.7; standard deviation: 3.56

L. mean: 5; median: 4; mode: 4

T. range: 26; standard deviation: 10.54

E. range: 25; standard deviation: 9.27

G. mean: 52; median: 48; mode: 48

S. mean: 13; median: 13; mode: none

11.1

7 1 4 11 5 9 2 6 10 3 8


11.2 Start Thinking

Using a printout from your teacher, obtain a list of your percentages on tests in your math class for the current school year. Arrange the percentages from least to greatest. Find the lowest percentage, the highest percentage, and the median of the test scores. Plot all three on a number line. Find the median of the lower half of your test scores (the numbers from the lowest score to the original median) and the median of the upper half of your test scores (the numbers from the original median to the highest score). Plot these data points on the number line. Are all the numbers on the number line equidistant? Why or why not?

Find the median of the data.

1. 3, 5, 9, 10, 15

2. 1, 4, 3, 6, 1, 5, 5, 6−

3. 15, 19, 19, 26, 16, 23, 22, 22

4. 3, 1, 4, 3, 0, 2, 1, 1, 1, 2, 5− − − −

5. 215, 4, 296, 29, 6, 215, 219, 281

6. 2, 2, 4, 3, 4, 2

Complete the square for the expression. Then factor the trinomial.

1. 2 11x x+ 2. 2 15x x− 3. 2 6x x−

4. 2 13x x− 5. 2 5x x+ 6. 2 4x x+

11.2 Warm Up



395

11.2 Practice A

Name _________________________________________________________ Date __________

In Exercises 1–6, use the box-and-whisker plot to find the given measure.

1. least value 2. median 3. greatest value

4. third quartile 5. range 6. first quartile

In Exercises 7 and 8, make a box-and-whisker plot that represents the data.

7. Hours of exercise per week: 0, 7, 2, 5, 12, 2, 0, 9

8. Numbers of cars in a parking lot: 12, 35, 20, 17, 24, 30, 28, 16

9. The dot plot represents the numbers of customers at the tables in a restaurant. Make a box-and-whisker plot that represents the data.

10. The box-and-whisker plot represents a data set. Determine whether each statement is true. Explain your reasoning.

a. The data set contains the value 11.

b. The distribution is skewed left.

0 1 2 3 4 5 6 7 8

0 2 4 6 8 10 12

2 5 6 8 10

0 2 4 6 8 10 12

1 5 6 8 10


11.2 Practice B

Name _________________________________________________________ Date _________

In Exercises 1–6, use the box-and-whisker plot to find the given measure.

1. least value 2. range 3. first quartile

4. third quartile 5. greatest value 6. median

In Exercises 7 and 8, make a box-and-whisker plot that represents the data.

7. Numbers of chairs in a classroom: 30, 27, 32, 25, 12, 22, 20, 29, 35, 35, 28

8. Temperatures (in degrees Fahrenheit): 18, 0, 7, 8, 12, 15, 21, 0, 1, 3− − − −

9. The stem-and-leaf plot represents the heights (in inches) of pineapple plants in a garden. Make a box-and-whisker plot that represents the data.

10. The box-and-whisker plot represents a data set. Determine whether each statement is true. Explain your reasoning.

a. The median of the data is 15.

b. The distribution is symmetric.

Stem Leaf 0 4 7 7 8 9 1 0 0 0 2 5 6 9 2 0 1 Key: 1 | 0 10 inches

4 6 8 10 12 14 16

85 9 12 15

0 2 4 6 8 10 12 14 16 18 20

52 10 15 18


397


Name _________________________________________________________ Date __________

Too Much Screen Time? Collect data from your classmates and use your knowledge of central tendencies to analyze and interpret the data.

1. Record the approximate amount of time (in hours) each class member either watches TV or uses his or her smart phone or tablet per day.

2. List the results in order from least to greatest.

3. Can you tell from this list what the average may be and why?

4. Make a stem-and-leaf plot using the data.

5. Find the mean, median, mode, and range of the data.

6. Use the stem-and-leaf plot to find the first and third quartiles.

7. Construct a box-and-whisker plot with the information.

8. Find and interpret the range of this data.

9. Describe the distribution of the data.

10. Is the data more spread out in Q1 or Q2? Explain.


Puzzle Time

Name _________________________________________________________ Date _________

What Did The Tired Dishcloth Say To The Counter? Write the letter of each answer in the box containing the exercise number.

Identify the least value, Q1, Q2, Q3, and greatest value of the data set.

1. Time spent reading (in hours): 1, 2, 3, 4, 1, 3, 5, 4

2. Lengths of rabbits (in inches): 19, 15, 23, 22, 20, 19, 26, 24

3. Temperature changes ( )F :° 10, 8, 3, 4, 7, 5, 6, 8, 6, 5, 2− − − − − −

4. Sneaker prices (in dollars): 104, 75, 125, 90, 104, 320, 170, 134

Use the data set to complete the exercises.

10, 13, 14, 15, 12, 14, 16, 15

5. Find the first quartile.

O. 12.5 P. 15 Q. 16

6. Find the second quartile.

H. 12.5 I. 14 J. 16

7. Find the third quartile.

O. 12.5 P. 15 Q. 14

8. Find the range of the data.

V. 3.5 W. 6 X. 26

9. Describe the distribution of the data.

U. skewed left V. symmetric W. skewed right

10. Find the interquartile range.

D. 6 E. 2.5 F. 15

Answers

T. least value: 15; Q1: 19; Q2: 21; Q3: 23.5; greatest value: 26

D. least value: 75; Q1: 97; Q2: 114.5; Q3: 152; greatest value: 320

I. least value: 1; Q1: 1.5; Q2: 3; Q3: 4; greatest value: 5

M. least value: 10;− Q1: 6;− Q2: 2;− Q3: 5;greatest value: 8

11.2

6 , 3 8 1 7 10 4 5 9 2


399

11.3 Start Thinking 11.3 Start Thinking

Gather the following information from your classmates: • Height (in feet and inches) • Shoe size • Number of siblings

Use equal intervals to make a histogram for each set of data. Find the mean and median of each set of data. Mark these on the histogram, noting which bars contain each. Compare the mean and median for each. What does a histogram look like when the mean is larger? What does a histogram look like when the median is larger?

Find the mean, median, and mode of the data. If necessary, round to the nearest tenth.

1. 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14

2. 0, 6, 11, 21, 14, 8, 1 3. 1, 2, 5, 6, 9, 10, 13, 14, 17, 18, 21

4. 6, 6, 13, 13, 27, 44, 34 5. 0, 3, 2, 5, 4, 7

6. 0, 2, 2, 5, 7, 3, 2, 5, 6, 9

Find the inverse of the relation.

1. ( ) ( ) ( ) ( ) ( )2, 1 , 4, 9 , 5, 4 , 8, 6 , 10, 2− − − − −

2. ( ) ( ) ( ) ( ) ( )3, 0 , 5, 4 , 7, 6 , 9, 0 , 11, 5− −

3.

11.3 Warm Up


Input 4 4 1 6 11

Output 7 5 1 5 7


11.3 Practice A

Name _________________________________________________________ Date _________

1. The frequency table shows the results of a survey that asked people how many hours they spend working in the yard per month. Display the data in a histogram. Describe the shape of the distribution.

In Exercises 2 and 3, describe the shape of the distribution of the data. Explain your reasoning.

2. 3.

4. The table shows the last gas purchases at the pump.

a. Display the data in a histogram using six intervals beginning with 10–24.

b. Which measures of center and variation best represent the data? Explain.

Hours in yard 0–1 2–3 4–5 6–7 8–9 10–11

Frequency 28 35 25 15 12 4

Gas Purchases (dollars)

36 75 42 17 98 93 10

24 15 27 32 23 65 27

54 71 48 43 38 26 58

Stem Leaf 1 4 7 8 2 3 4 5 8 3 0 1 1 4 6 4 2 2 4 5 5 0 1 2 Key: 2 | 1 21

Stem Leaf 3 8 4 5 5 0 1 2 4 6 2 3 3 5 7 8 9 7 1 2 2 4 6 6 Key: 5 | 2 52


401

11.3 Practice B

Name _________________________________________________________ Date __________

1. The frequency table shows the results of a survey that asked people how many parking tickets they received during the last five years. Display the data in a histogram. Describe the shape of the distribution.

In Exercises 2 and 3, describe the shape of the distribution of the data. Explain your reasoning.

2. 3.

4. The table shows the results of a survey that asked sophomores and juniors how many school events they attended last month.

a. Make a double box-and-whisker plot that represents the data. Describe the shape of each distribution.

b. Compare the number of school events attended by sophomores to the number of school events attended by juniors.

c. About how many of the juniors surveyed would you expect to attend between 7 and 11 school events?

Sophomores Juniors

Survey size 55 52

Minimum 0 2

Maximum 9 15

1st Quartile 3 7

Median 6 12

3rd Quartile 8 14

Mean 9 11

Standard Deviation 2.4 4.3

Number of parking tickets 0–1 2–3 4–5 6–7 8–9 10–11

Frequency 18 23 20 14 4 1

Stem Leaf 1 2 3 4 5 6 7 8 9 2 0 1 2 3 4 5 6 7 8 9 3 0 1 2 3 4 5 6 4 0 1 7 8 9 5 2 3 6 4 7 5 Key: 2 | 1 21

Stem Leaf 3 8 4 4 5 5 5 0 2 4 4 5 6 2 3 4 5 5 8 9 7 2 4 6 6 7 8 1 3 3 9 4 Key: 4 | 5 45



Name _________________________________________________________ Date _________

Calculate Standard Deviation of a Population The standard deviation is a measure of how spread out the numbers are in a data set. By definition the formula for standard deviation is the square root of the variance. Well, what is variance? Variance is defined as the average of the squared differences of the mean. First, to calculate the variance, find the mean. Then for each number in your data set, subtract the mean and square the number. After this, find the average of these squared differences. Your solution will be the variance of the data set. To calculate the value of the standard deviation, take the square root of the variance.

Example: Calculate the standard deviation for the data set 3, 4, 5, 7, 8, 9.

First, find the mean: 3 4 5 7 8 9 36 66 6

+ + + + + = =

Second, find the variance:

( ) ( ) ( ) ( ) ( ) ( )2 2 2 2 2 23 6 4 6 5 6 7 6 8 6 9 6 9 4 1 1 4 96 6

286243

− + − + − + − + − + − + + + + +=

=

=

Take the square root to calculate the standard deviation: 24 2.163

≈

Calculate the mean and the approximate population standard deviation of the data set. Round to the nearest thousandth, when necessary.

1. 75, 83, 96, 100, 121, and 125

2. the first 8 natural numbers (1 through 8)

3. the first 5 numbers of the Fibonacci sequence ( )1, 1, 2, 3, 5

4. the test scores of six friends: 56, 65, 70, 72, 81, and 82


403

Puzzle Time

Name _________________________________________________________ Date __________

What Can You Put Into A Barrel Full Of Water To Make It Lighter? Write the letter of each answer in the box containing the exercise number.

Describe the shape of the distribution.

1.

K. skewed left L. skewed right M. symmetric

2.

M. skewed left N. skewed right O. symmetric

3.

A. skewed left B. skewed right C. symmetric

4.

C. skewed left D. skewed right E. symmetric

5.

G. skewed left H. skewed right I. symmetric

11.3

Number of books read in a month 1–2 3–4 5–6 7–8 9–10

Frequency 15 12 10 3 1

Number of pets in a household 0–1 2–3 4–5 6–7 8–9

Frequency 1 3 6 3 1

Number of emails received 0–4 5–9 10–14 15–19 20–24


Test scores 51–60 61–70 71–80 81–90 91–100


Number of songs downloaded in a week 1–3 4–6 7–9 10–12 13–15


3 5 2 1 4


11.4 Start Thinking

Brainstorm a question with only two possible answers and ask the question to each person in your class. Track the answers in a table with boys and girls as row headings and answer 1 and answer 2 (specific to your question) as column headings. The resulting table should have four boxes for answers.

This is called a two-way table. Use your table as evidence to explain how the name is related to the look of the table. Count the number of people surveyed for the table. Is there a way to know the total by looking at the table? Explain why or why not.

Write the fraction in simplest form.

1. 820 2. 21

42 3. 6298 4. 6

4

5. 36 6. 12

15 7. 7698 8. 162

99

9. 129 10. 2

2 11. 91 12. 2

8

Solve the equation. Check your solution.

1. ( ) ( )8 4 2 7g g− = − 2. ( ) ( )8 1 5 14t t− + = +

3. ( ) ( )32 4 8 1 5 10x x− = − − 4. ( ) ( )4

32 3 3 27 9t t− − = −

5. ( ) ( )9 3 1 3 7 9y y− = + 6. ( )3 3 7 3 13x x x− = +

11.4 Warm Up



405

11.4 Practice A

Name _________________________________________________________ Date __________

You conduct a survey that asks 253 students about whether they ride a bicycle to school. In Exercises 1–4, use the results of the survey shown in the two-way table.

1. How many freshmen were surveyed?

2. How many sophomores were surveyed?

3. How many students ride a bicycle to school?

4. How many students do not ride a bicycle to school?

In Exercises 5 and 6, find and interpret the marginal frequencies.

5. 6.

7. Refer to Exercise 5.

a. What percent of students surf?

b. What percent of students do not skateboard?

c. What percent of students who surf also skateboard?

d. What percent of students neither surf nor skateboard?

Skateboard

Yes No

Surf

Yes 32 65

No 45 24

Ride Bike to School

Yes No C

lass

Freshman 54 72

Sophomore 5 122

Pet

Yes No

Job Yes 74 13

No 153 32


11.4 Practice B

Name _________________________________________________________ Date _________

In Exercises 1 and 2, find and interpret the marginal frequencies.

1. 2.

In Exercises 3 and 4, complete the two-way table.

3.

4.

5. You conduct a survey that asks 397 students in your school about whether they have played a musical instrument or participated in a sport. One hundred eighteen students have played a musical instrument and 57 of those students have participated in a sport. Thirty-four of the students have not played a musical instrument or participated in a sport. Organize the results in a two-way table. Include the marginal frequencies.

Coffee

Yes No

Tea Yes 33 112

No 24 20

Airplane

Yes No

Trai

n Yes 5 3

No 278 321

Participated in a Triathlon

Yes No Total

Gen

der Female 24 137

Male 142

Total 306

Dual Enrollment Student

Yes No Total

Cla

ss Sophomore 247

Senior 83

Total 432 550


407


Name _________________________________________________________ Date __________

Logic Puzzle Complete the logic puzzle using the information given.

After class, a group of friends went to the school café for a snack. Match each person to their drink and fruit order, and determine the final bill for each.

1. The person who had the milk paid $1 more than Wendy.

2. Ruby paid more than the person who had the milk.

3. The person who ordered the banana was either the person who had the milk or the person who paid $5.99.

4. The four friends were the person who paid $8.99, the person who ordered the apple, the person who ordered the grapefruit, and Wendy.

5. Tom paid $1 more than the person who ordered the grapefruit.

6. The person who ordered the grapefruit paid $2 more than the person who had the water.

7. The person who paid $7.99 was either the person who had the iced tea or the person who had the water.

Fran

k

Rub

y

Tom

Wen

dy

milk

gree

n te

a

wat

er

iced

tea

bana

na

appl

e

man

go

grap

efru

it

$5.99

$6.99

$7.99

$8.99

banana

apple

mango

grapefruit

milk

green tea

water

iced tea


Puzzle Time

Name _________________________________________________________ Date _________

What Has A Head And Tail But No Body? Write the letter of each answer in the box containing the exercise number.

Your assignment is to survey 320 students about whether they ride a bus to school. Use the results of the survey to answer the questions that follow the table.

1. How many juniors were surveyed?

2. How many seniors were surveyed?

3. How many students ride a bus to school?

4. How many students do not ride a bus to school?

5. Given that a student rides a bus to school, what is the approximate conditional relative frequency that he or she is a junior?

6. Given that a student rides a bus to school, what is the approximate conditional relative frequency that he or she is a senior?

7. Given that a student does not ride a bus to school, what is the approximate conditional relative frequency that he or she is a junior?

8. Given that a student does not ride a bus to school, what is the approximate conditional relative frequency that he or she is a senior?

Answers

T. 26%

A. 144

R. 74%

Q. 62%

R. 152

U. 38%

E. 176

A. 168

11.4

4 8 7 2 5 6 1 3

Ride A Bus To School

Yes No

Class Juniors 112 64

Seniors 40 104


409

11.5 Start Thinking

You are going to survey your classmates, asking them which video game system is their favorite. The students will have five choices, including “none.” Which of the following types of graphs could you choose to display the data? In your opinion, which is the best choice and why?

• bar graph • box-and-whisker plot • circle graph • dot plot • histogram

Determine whether the data is discrete or continuous. Explain.

1. a person’s height over time

2. the number of students at each basketball game

Evaluate the function when x 1 and 6.= −

1. ( ) 5f x x= − 2. ( ) 8h x x= − −

3. ( ) 2 3p x x= − − 4. ( ) 13 6v x x= + +

11.5 Warm Up


• line graph • pictograph • scatter plot • stem-and-leaf plot


11.5 Practice A

Name _________________________________________________________ Date _________

In Exercises 1–4, tell whether the data are qualitative or quantitative. Explain your reasoning.

1. basic costs of monthly Internet access

2. breeds of dogs at a kennel

3. apartment numbers in an apartment building

4. heights of students in a 1st grade class

In Exercises 5 and 6, choose an appropriate data display for the situation. Explain your reasoning.

5. the number of cars in the parking lot over a 30-day period

6. the distribution of students according to class

In Exercises 7 and 8, analyze the data and then create a display that best represents the data. Explain your reasoning.

7.

8.

Average Temperature (degrees Fahrenheit)

January 2 July 84

February 6 August 87

March 25 September 62

April 56 October 57

May 65 November 34

June 76 December 12

Vegetable Plants in Your Garden

Tomato 20 Green Pepper 10

Onion 25 Zucchini 6

Corn 20 Squash 7

Carrots 30 Cucumbers 10


411

11.5 Practice B

Name _________________________________________________________ Date __________

In Exercises 1–4, tell whether the data are qualitative or quantitative. Explain your reasoning.

1. numbers of cans of vegetables at a food pantry

2. names of players on your school soccer team

3. balances in the savings accounts at a bank

4. numbers on the back of the jerseys of your school football team

In Exercises 5 and 6, choose an appropriate data display for the situation. Explain your reasoning.

5. bowling scores for all of the students on the team

6. the price of a gallon of gas on January 1st over a 10-year period

In Exercises 7 and 8, describe how the graph is misleading. Then explain how someone might misinterpret the graph.

7.

8.

Named Winter Storms

Freq

uen

cy

02006 2007 2008 2010 2011 2012

20

10

Year

6 85

12 14

7

5 8 17 26 31



Name _________________________________________________________ Date _________

Geometric Probability What is the chance that a needle dropped on a figure at random would hit the shaded region? Problems like this have become known as geometric probability.

Example: Find the probability that a randomly chosen point on the figure lies within the shaded region. Use the formula for the

area of a trapezoid, ( )1 21 ,2

A b b h= + to find the total area of

the figure. Then find the area of the shaded region by using the

formula for the area of a triangle: 12

A bh= . The geometric

probability is the area of the shaded region over the total area of the figure.

Area of figure: ( )1 10 7 6 51 square units2

A = + • =

Area of triangles: ( )( )1 1.5 6 4.5 4.5 2 9 square units2

A = = → • =

Geometric probability: 9 3 17.6%51 17

= ≈

Find the probability that a randomly chosen point on the figure lies within the shaded region. Round to the nearest tenth, when necessary.

1. 2.

3. 4.

6

7

10

8

8

10

6

62

8

62


413

Puzzle Time

Name _________________________________________________________ Date __________

What Goes Up But Never Comes Down? Write the letter of each answer in the box containing the exercise number.

Tell whether the data are qualitative or quantitative.

1. prices of cell phones at a store

Q. qualitative R. quantitative

2. student identification numbers

E. qualitative F. quantitative

3. the favorite food of students in your class

O. qualitative P. quantitative

4. ages of students in your class

X. qualitative Y. quantitative

Choose the most appropriate data display for the situation.

5. the number of students entering kindergarten each year

F. circle graph G. line graph H. dot plot

6. the favorite academic subject of students in your class

A. circle graph B. box-and-whisker plot C. bar graph

7. the ages of students in your class

T. circle graph U. stem-and-leaf plot V. scatter plot

11.5

4 3 7 1 6 5 2


Chapter

11 Cumulative Review

Name _________________________________________________________ Date _________

Solve the equation, if possible.

1. ( ) ( )2 2 4 2 3 3 8 4x x x x x x+ − + = + − +

2. 2 2 2 2 2y − − =

Solve the inequality, if possible.

3. 8 16 24h + ≤ − 4. ( )10 3 4 5x≥ − + − 5. 8 16 24x + > −

6. You sell magazine subscriptions and earn $2 for every new subscriber you sign up. You also earn a $30 weekly bonus regardless of how many magazine subscriptions you sell. If you want to earn at least $98 this week, what is the minimum number of subscriptions you need to sell?

7. Four times the quantity of a number x minus 8 is no more than 50. Write this sentence as an inequality.

Graph the linear equation or linear inequality.

8. 3 4y x= − 9. 4 2 10x y− > − 10. ( )4 3 1y x− = −

Write an equation of the line in point-slope form that passes through the given point and is perpendicular to the given line.

11. ( )1, 5 ; 8y x− = +

12. ( ) ( )12, 4 ; 7 84

y x− − = +

13. ( )8, 0 ; 10 5 15x y− − =

Solve the system of linear equations by graphing, substitution, or elimination.

14. 1 452 4

y x

y x

= +

= +

15. 2 198

x yx y

+ =− =

16. 5 73 2 12

y xx y= −

− − = −

17. The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

Simplify the expression. Write your answer using only positive exponents.

18. ( )( )

4

1

2xx x

−

− 19. ( )12 4

32x x

x

−

− 20. ( )( )2 4 2 4

3 2

2 4 3

3

x y x y xx y−


415

Chapter

11 Cumulative Review (continued)

Name _________________________________________________________ Date __________


21. 5 11 47 7x− = 22. 2 6 105 5x x+ += 23. 7 102 4x x +=

Find the sum or the difference.

24. ( ) ( )17 42g g+ + − − 25. ( ) ( )2 7 8 15y y− − − −

Find the product.

26. ( )( )1 5x x− − 27. ( )24 3x y−

Factor the polynomial.

28. 2 4 21m m+ − 29. 2 15 44z z− + 30. 24 44 96w w+ +

31. A coin is dropped from the top of a building. The distance d (in feet) between the coin and the ground t seconds after it is dropped is given by 216 144.d t= − + How long after the coin is dropped does it hit the ground?

Solve the equation.

32. 2 100 0z − = 33. 2 27 50 0y y+ + =

Factor the polynomial completely.

34. 3 26 15 2 5x x x− + − 35. 3 2 1y y y+ + +

Graph the function. Compare the graph to the graph of ( )f x x 2= .

36. ( ) 213

h x x= 37. ( ) 27 1p x x= − + 38. ( ) 2 2q x x= −

39. The function ( ) 2016f t t s= − + represents the approximate height (in feet) of an

object falling t seconds after it is dropped from an initial height 0s (in feet). A ball is dropped from a height of 784 feet.

a. After how many seconds does the ball hit the ground?

b. Suppose the initial height is adjusted by k feet. How will this affect part (a)?

Tell whether the function has a minimum value or a maximum value. Then find the value.

40. ( ) 24 24 15f x x x= − − + 41. ( ) 26 36 20f x x x= + −


Chapter

11 Cumulative Review (continued)

Name _________________________________________________________ Date _________

Find the vertex and the axis of symmetry of the graph of the function.

42. ( ) ( )210 3f x x= − 43. ( ) 20.125g x x= 44. ( ) ( )28 6 2g x x= − + +

Graph the function. Compare the graph to the graph of ( )f x x 2 .=

45. ( ) ( )21 63

f x x= + 46. ( ) ( )22 1 7f x x= − −

Simplify the expression.

47. 10

33

1288

xy

48. 55 3 3− −

49. 2 20 2 18 2 5− + −

Solve the equation by graphing.

50. 2 2 3 0x x− − = 51. 2 10 7x x+ =

Solve the equation using square roots.

52. 27 112x = 53. 2 49x− = − 54. 24 17 53x + =

Solve the equation by completing the square.

55. 2 8 21 6x x− + = 56. 2 19 66 6y y+ + =

57. You want to enclose a rectangular vegetable garden with 100 feet of fence, with one side of the garden being your garage. How should you lay out the fence to maximize the area of the garden?

Solve the equation using the Quadratic Formula. Round your solutions to the nearest tenth, if necessary.

58. 22 4 3 0x x− − = 59. 2 4 6 2y y− − =

Solve the system of equations by graphing, elimination, or substitution, if possible.

60. 2 3 53

y x xy x

= + −= +

61. 2 11

y xy x

= +− =

62. 2 123

y x xy x

= − −= +

63. The area of a rectangular pool cover at a local park is 360 square meters. The width of the pool cover is 2 meters shorter than the length. Find the dimensions of the pool cover in meters.


417

Chapter

4 Cumulative Review Cumulative Review (continued) Chapter

11

Name _________________________________________________________ Date __________

Describe the domain of the function.

64. 23

y x= 65. 4y x= − 66. ( ) 3 2 411

f x x= − +

Graph the function. Describe the range.

67. ( ) 4f x x= − 68. ( ) 7f x x= + 69. ( ) 27

h x x=

Graph the function. Compare the graph to the graph of f x x3( ) .=

70. ( ) 30.5 3 7d x x= − + 71. ( ) 33 2 1c x x= + −


72. 3 5 10w + − = 73. 7 9 35r + = 74. 5 10 3 18x x+ = +

Find the inverse of the given function.

75. ( ) 3 15

f x x= − 76. ( ) 7 8f x x= −

Find the mean, median, and mode of the data set. Which measure of center best represents the data? Explain.

77. 13, 18, 13, 14, 13, 16, 14, 21, 13 78. 23, 29, 20, 32, 23, 21, 33, 25

79. Make a box-and-whisker plot that represents the data.

Miles traveled to work 14, 6, 3, 2, 4, 15, 11, 8, 1, 7, 2, 1, 3, 4, 10, 22, 20

80. Describe the shape of the distribution of the data. Explain your reasoning.

Tell whether the data are qualitative or quantitative.

81. everyone’s favorite color in your class 82. jersey numbers on a football team

83. It is the end of the school year in math class, and your grades for the four quarters are as follows: 87, 71, 95, and 92. Your final test counts as a fifth of your final grade, as do your grades for the four quarters. What grade do you need on your final test in order to get an 85 for the year?

Stem Leaf 1 1 1 8 2 1 3 5 5 8

3 2 6 7

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