Algebra 1A Unit 05...Unit 05 Sections 1.9, 2.5, 2.6 GUIDED NOTES NAME ___ Teacher _ Period ___ 1. Section 1-9: Analyzing Tables and Graphs Why are graphs used to display data?

1

Algebra 1A

Unit 05 Sections 1.9, 2.5, 2.6

GUIDED NOTES

NAME _________________________

Teacher _______________

Period ___________

1

Section 1-9: Analyzing Tables and Graphs

Why are graphs used to display data?

Why are tables used to display data?

Example 1: Use the graph to answer the questions.

a) Describe how you can tell from the graph that the number of men in NCAA sports remained about

the same, while the number of women increased?

b) Approximately how many more men than women participated in sports during the 1997

school year?

c) Which is better to use to answer part b

d) What was the total participation among men and women in the 2000

e) Why did you need to use the table to answer part d?

2

Date: ______________________

9: Analyzing Tables and GraphsNotes


Describe how you can tell from the graph that the number of men in NCAA sports remained about

the same, while the number of women increased?

Approximately how many more men than women participated in sports during the 1997

Which is better to use to answer part b – the graph or the table?

What was the total participation among men and women in the 2000 – 2001 academic ye

Why did you need to use the table to answer part d?

Date: ______________________

9: Analyzing Tables and Graphs

Describe how you can tell from the graph that the number of men in NCAA sports remained about

Approximately how many more men than women participated in sports during the 1997 – 1998

2001 academic year?

2

Example 2: A recent poll in New York asked residents whether cell phone use

while driving should be banned. The results are show in the circle graph.

a) If 250 people in New York were surveyed, a

think that cell phone use while driving should be banned? Show all work.

b) If a city of 516,000 is representative of those surveyed, how many people could be expected not to know

whether cell phone use while driving should be banned?


a) How would the change in enrollment between 1997 and 1999 compare

to the change in enrollment between 1995 and 1999? Show all work.

b) Why can’t you simply extend the line on the gr

enrolled in 2005?

Example 4: Joel used the graph below to show his algebra grade for the first four reporting periods of the year.

Does the graph misrepresent the data? Explain in sentences.

3

Example 2: A recent poll in New York asked residents whether cell phone use

while driving should be banned. The results are show in the circle graph.

If 250 people in New York were surveyed, about how many would

think that cell phone use while driving should be banned? Show all work.

If a city of 516,000 is representative of those surveyed, how many people could be expected not to know

whether cell phone use while driving should be banned? Show all work.


How would the change in enrollment between 1997 and 1999 compare

to the change in enrollment between 1995 and 1999? Show all work.

Why can’t you simply extend the line on the graph beyond 1999 to predict the number of students


Does the graph misrepresent the data? Explain in sentences.

If a city of 516,000 is representative of those surveyed, how many people could be expected not to know

aph beyond 1999 to predict the number of students


3

Section 2-5: Displaying and Analyzing Data

1. What was the most popular

boys’ name in all five decades?

2. How can you tell?

3. Were any girls’ names as

popular as Michael?

4. How can you tell?

Example 1: Draw a line plot for the data. Which number occurs the most frequently?

11, - 2, 10, -2, 7, 2, 7, 4, 9, 0, 6, 9, 7, 2, 0, 4, 10, 7, 6, 9

Example 2: The highway patrol did a radar survey of the speeds of cars along a stretch of

minute. The speeds (in miles per hour) of the 20 cars that passed are listed below.

72, 70, 72, 74, 68, 69, 70, 72, 74, 75, 79, 75, 74, 72, 70, 64, 69, 66, 68, 67

a) Make a line plot of the data.

b) Which speed occurs the most frequently?

4

Date: ______________________

5: Displaying and Analyzing DataNotes – Part 1

Example 1: Draw a line plot for the data. Which number occurs the most frequently?

2, 7, 2, 7, 4, 9, 0, 6, 9, 7, 2, 0, 4, 10, 7, 6, 9

Example 2: The highway patrol did a radar survey of the speeds of cars along a stretch of

minute. The speeds (in miles per hour) of the 20 cars that passed are listed below.

72, 70, 72, 74, 68, 69, 70, 72, 74, 75, 79, 75, 74, 72, 70, 64, 69, 66, 68, 67

Which speed occurs the most frequently?

Date: ______________________

5: Displaying and Analyzing Data

Example 2: The highway patrol did a radar survey of the speeds of cars along a stretch of highway for 1

4

Example 3: Use the data below to make a stem and leaf plot.

85, 78, 100, 99, 108, 115, 131, 121, 116, 93, 126, 114, 123, 79, 84,

92, 92, 131, 90, 75, 104, 85, 88, 110, 70, 107, 116, 97, 129, 132

Example 4: Monique wants to compare the monthly ave

she decides which city she wants to move. The table shows the monthly average high temperatures for both

cities.

a) Make a stem and leaf plot to compare the data.

b) What is the difference between the

c) Which city has higher average temperatures?

5

ample 3: Use the data below to make a stem and leaf plot.

85, 78, 100, 99, 108, 115, 131, 121, 116, 93, 126, 114, 123, 79, 84,

92, 92, 131, 90, 75, 104, 85, 88, 110, 70, 107, 116, 97, 129, 132

Example 4: Monique wants to compare the monthly average high temperatures of Dallas and Atlanta before


Make a stem and leaf plot to compare the data.

What is the difference between the highest average temperatures in each city?

Which city has higher average temperatures?

rage high temperatures of Dallas and Atlanta before


5

Section 2-5: Displaying and Analyzing Data

Measures of Central Tendency:

Mean:

Median:

Mode:

Example 1: The numbers below show the ages of the US Presidents since 1900 at the time they were

inaugurated. Which measure of central tendency best represents the data? Show all work.

Example 2: Which measure of central tendency best represents the data? S

6

Date: ______________________

5: Displaying and Analyzing DataNotes – Part 2

numbers below show the ages of the US Presidents since 1900 at the time they were


Example 2: Which measure of central tendency best represents the data? Show all work.

Date: ______________________

5: Displaying and Analyzing Data

numbers below show the ages of the US Presidents since 1900 at the time they were


how all work.

6

Example 3: The number of electoral votes for the 12 most populous states in the 2000 Presidential election are

listed below. Which measure of central tendency best represents the data? Show all work.

21, 22, 18, 23, 15, 25, 14, 32,


7



21, 22, 18, 23, 15, 25, 14, 32, 13, 33, 13, 54





7

8

Date: ______________________

Section 2-6: Probability: Simple Probability and Odds Notes – Part 1

PROBABILITY :

Probability –

Simple Event –

Sample Space –

Example 1: Find the probability of rolling a 4 on a die.

Example 2: Find the probability of rolling a number greater than two on a die.

Example 3: Find the probability of rolling an even number on a die.

Example 4: A class contains 6 students with black hair, 8 with brown hair, four with blonde hair and two with

red hair. Find P (black).


red hair. Find P (red or brown).

8

9


red hair. Find P (not blonde).

Example 7: A bowl contains 5 red chips, 7 blue chips, 6 yellow chips and 10 green chips. One chip is

randomly drawn. Find the probability that the chip is blue.


randomly drawn. Find P (red or yellow).


randomly drawn. Find the probability that the chip is not green.

9

10

Date: ______________________

Section 2-6: Probability: Simple Probability and Odds Notes – Part 2

ODDS:

Odds:

Example 1: Find the odds of rolling a number less than 3 on a die.

Example 2: Find the odds of rolling a number greater than 2 on a die.

Example 3: A weather forecast states that the probability of rain the next day is 40%. What are the odds that it

will rain?

10

11

Example 4: Melvin is waiting to board a flight to Washington, DC. According to the airline, the flight he is

waiting for is on time 80% of the time it flies. What are the odds that the plane will be on time?

Example 5: A card is selected at random from a standard deck of 52 cards. What are the odds against selecting

a 3?

Example 6: A card is selected at random from a standard deck of 52 cards. What are the odds against selecting

a 2 or a 5?

11

Study Guide and Intervention

Statistics: Analyzing Data by Using Tables and Graphs

NAME ______________________________________________ DATE______________ PERIOD _____

1-91-9

© Glencoe/McGraw-Hill 49 Glencoe Algebra 1

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on

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Analyze Data Graphs or tables can be used to display data. A bar graph comparesdifferent categories of data, while a circle graph compares parts of a set of data as apercent of the whole set. A line graph is useful to show how a data set changes over time.

The circle graph at the right shows the

number of international visitors to the United States

in 2000, by country.

a. If there were a total of 50,891,000 visitors, how

many were from Mexico?

50,891,000 3 20% 5 10,178,200

b. If the percentage of visitors from each country

remains the same each year, how many visitors

from Canada would you expect in the year 2003

if the total is 59,000,000 visitors?

59,000,000 3 29% 5 17,110,000

1. The graph shows the use of imported steel by U. S.companies over a 10-year period.

a. Describe the general trend in the graph. The general trend is an increase in the use ofimported steel over the 10-year period, withslight decreases in 1996 and 2000.

b. What would be a reasonable prediction for the percentage of imported steel used in 2002?about 30%

2. The table shows the percentage of change in worker productivity at the beginning of each year for a 5-year period.

a. Which year shows the greatest percentage increase in productivity? 1998

b. What does the negative percent in the first quarter of 2001 indicate? Worker productivity decreased in this period, as compared to the productivity one year earlier.

Source: Chicago Tribune

Worker Productivity Index

Year (1st Qtr.) % of Change

1997 11

1998 14.6

1999 12

2000 12.1

2001 21.2

Imported Steel asPercent of Total Used

Year

Perc

en

t

1990 1994 1998

40

30

20

10

0

Source: Chicago Tribune

Canada29%

Mexico20%

International Visitorsto the U.S., 2000

Others32%

UnitedKingdom

9% Japan10%

Source: TInet

ExampleExample

ExercisesExercises

12


Misleading Graphs Graphs are very useful for displaying data. However, some graphscan be confusing, easily misunderstood, and lead to false assumptions. These graphs may bemislabeled or contain incorrect data. Or they may be constructed to make one set of dataappear greater than another set.

The graph at the right shows the

number of students per computer in the U.S. public

schools for the school years from 1995 to 1999.

Explain how the graph misrepresents the data.

The values are difficult to read because the vertical scale is too condensed. It would be more appropriate to let each unit on the vertical scale represent 1 student rather than 5 students and have the scale go from 0 to 12.

Explain how each graph misrepresents the data.

1. The graph below shows the U.S. 2. The graph below shows the amount ofgreenhouse gases emissions for 1999. money spent on tourism for 1998-99.

The graph is misleading because The graph is misleading becausethe sum of the percentages is not the vertical axis starts at 400100%. Another section needs to billion. This gives the impressionbe added to account for the that $400 billion is a minimummissing 1%, or 3.68. amount spent on tourism.

World Tourism Receipts

Year

Billio

ns

of

$

1995 1997 1999

460

440

420

400

Source: The World Almanac

U.S. GreenhouseGas Emissions 1999

CarbonDioxide

82%

Nitrous Oxide6%

Methane9%

HCFs, PFCs, andSulfur Hexafluoride

2%

Source: Department of Energy

Students per Computer,U.S. Public Schools

Years since 1994

Stu

den

ts

1 2 3 4 5 6

20

15

10

5

0

Source: The World Almanac

Study Guide and Intervention (continued)


NAME ______________________________________________ DATE______________ PERIOD _____

1-91-9

ExercisesExercises

ExampleExample

13

Skills Practice


NAME ______________________________________________ DATE______________ PERIOD _____

1-91-9


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DAILY LIFE For Exercises 1–3, use the circle graph

that shows the percent of time Keisha spends on

activities in a 24-hour day.

1. What percent of her day does Keisha spend in the combined activities of school and doing homework? 50%

2. How many hours per day does Keisha spend at school? 9 h

3. How many hours does Keisha spend on leisure and meals? 3 h

PASTA FAVORITES For Exercises 4–8, use the table and bar graph that show the

results of two surveys asking people their favorite type of pasta.

4. According to the graph, what is the ranking for favorite pasta in both surveys?The ranking is the same for both: spaghetti, fettuccine, linguine.

5. In Survey 1, the number of votes for spaghetti is twice the number of votes for whichpasta in Survey 2? linguine

6. How many more people preferred spaghetti in Survey 2 than preferred spaghetti inSurvey 1? 10 people

7. How many more people preferred fettuccine to linguine in Survey 1? 6 people

8. If you want to know the exact number of people who preferred spaghetti over linguine in Survey 1, which is a better source, the table or the graph? Explain.The table, because it gives exact numbers.

PLANT GROWTH For Exercises 9 and 10, use the line

graph that shows the growth of a Ponderosa pine over

5 years.

9. Explain how the graph misrepresents the data.The vertical axis begins at 10, making it appear that the tree grew much faster compared to its initial height than it actually did.

10. How can the graph be redrawn so that it is not misleading?To reflect accurate proportions, the vertical axisshould begin at 0.

Growth of Pine Tree

Years

He

igh

t (f

t)

1 2 3 4 5 6

16

15

14

13

12

11

10

Pasta Favorites

5

Spaghetti

Fettucine

Linguine

10 15 20 25 30 35 40 45 500

Number of People

Survey 1Survey 2

Spaghetti Fettuccine Linguine

Survey 1 40 34 28

Survey 2 50 30 20

School37.5%

Sleep37.5%

Leisure4.5%Meals

8%

Homework12.5%

Keisha’s Day

14


MINERAL IDENTIFICATION For Exercises 1–4, use the following information.

The table shows Moh’s hardness scale, used as a guide to help identify minerals. If mineral A scratches mineral B, then A’s hardness number is greater than B’s. If B cannot scratch A,then B’s hardness number is less than or equal to A’s.

1. Which mineral(s) will fluorite scratch? talc, gypsum, calcite

2. A fingernail has a hardness of 2.5. Which mineral(s) will itscratch? talc, gypsum

3. Suppose quartz will not scratch an unknown mineral. What is the hardness of the unknown mineral? at least 7

4. If an unknown mineral scratches all the minerals in the scale up to 7, and corundum scratches the unknown, what is thehardness of the unknown? between 7 and 9

SALES For Exercises 5 and 6, use the line graph that

shows CD sales at Berry’s Music for the years 1998–2002.

5. Which one-year period shows the greatest growth in sales?from 1999 to 2000

6. Describe the sales trend. Sales started off at about6000 in 1998, then dipped in 1999, showed a sharpincrease in 2000, then a steady increase to 2002.

MOVIE PREFERENCES For Exercises 7–9, use the circle

graph that shows the percent of people who prefer

certain types of movies.

7. If 400 people were surveyed, how many chose action movies as their favorite? 180

8. Of 1000 people at a movie theater on a weekend, how many would you expect to prefer drama? 305

9. What percent of people chose a category other than action or drama? 24.5%

TICKET SALES For Exercises 10 and 11, use the bar graph

that compares annual sports ticket sales at Mars High.

10. Describe why the graph is misleading. Beginning the vertical axis at 20 instead of 0 makes the relative sales for volleyball and track and field seem low.

11. What could be done to make the graph more accurate?Start the vertical axis at 0.

Ticket Sales100

80

60

40

20

Basketb

all

Footb

all

Track

& Fi

eld

Volleyb

all

Tic

kets

So

ld(h

un

dre

ds)

Action45%

Drama30.5%

Comedy14%

Foreign0.5%

ScienceFiction10%

Movie Preferences

CD Sales

Year

Tota

l Sale

s(t

ho

usa

nd

s)

1998 2000 2002

10

8

6

4

2

0

Mineral Hardness

Talc 1

Gypsum 2

Calcite 3

Fluorite 4

Apatite 5

Orthoclase 6

Quartz 7

Topaz 8

Corundum 9

Diamond 10

Practice (Average)


NAME ______________________________________________ DATE______________ PERIOD _____

1-91-9

15


Statistics: Displaying and Analyzing Data

NAME ______________________________________________ DATE ____________ PERIOD _____

2-52-5


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Create Line Plots and Stem-and-Leaf Plots One way to display data graphicallyis with a line plot. A line plot is a number line labeled with a scale that includes all thedata and 3s placed above a data point each time it occurs in the data list. The 3s representthe frequency of the data. A stem-and-leaf plot can also be used to organize data. Thegreatest common place value is called the stem, and the numbers in the next greatest placevalue form the leaves.

Draw a line plot for

the data.

23 3 4 7 9 10 22 3

6 4 3 9 21 22 4 2

Step 1 The value of the data ranges from23 to 10, so construct a number linecontaining those points.

Step 2 Then place an 3 above the numbereach time it occurs.

76543210212223

3 3 3 3 3 3 3 3 3

3 3 3

3 3

3

3

8 9 10

76543210212223 8 9 10

Use the data below to

create a stem-and-leaf plot.

62 74 89 102 92 65 68 98 78 65

78 80 83 93 87 89 104 109 104

68 97 68 64 98 93 90 102 104

The greatest common place value is tens, sothe digits in the tens place are the stems.Thus 62 would have a stem of 6 and 104would have a stem of ten. The stem-and-leafplot is shown below.

Stem | Leaf

6 | 2 4 5 5 8 8 87 | 4 8 88 | 0 3 7 9 99 | 0 2 3 3 7 8 8

10 | 2 2 4 4 4 9 62 5 62

Example 1Example 1 Example 2Example 2

ExercisesExercises

Use the table at the right for Exercises 1–3.

1. Make a line plot representing the weights of the wrestlers shown in the table at the right.

2. How many wrestlers weigh over 140 lb?

3. What is the greatest weight?

Use each set of data to make a stem-and-leaf plot.

4. 32 45 41 29 30 30 31 34 38 5. 102 104 99 109 108 112 115 120 36 32 34 41 40 42 41 29 30 112 114 98 94 96 101 100 102

200190180170160150140130120110100

3 3 3 3

3 3

3

3 3 3

3 3

3 33

Weights of Junior Varsity Wrestlers (pounds)

170 160 135 135 160 122 188 154

108 135 140 122 103 190 154

16


Analyze Data Numbers that represent the centralized, or middle, value of a set of dataare called measures of central tendency. Three measures of central tendency are themean, median, and mode.

Definition Example

MeanSum of the data values divided by the

Data: 24, 36, 21, 30, 21, 30; 5 27number of values in the data set.

The middle number in a data set when

the numbers are arranged in numerical

Median order. If there is an even number of Data: 21, 21, 25, 30, 31, 42; 5 27.5

values, the median is halfway between

the two middle values.

ModeThe number or numbers that occur

Data: 21, 21, 24, 30, 30, 36; 21 and 30 are modesmost often in the set of data.

Which measure of central tendency best represents the data?

Find the mean, median, and mode.

Mean 5 105

Median 5 102

Modes 5 99 and 112

The median best represents the center of the data since the mean is too high.

Find the mean, median, and mode for each data set. Then tell which best

represents the data.

1. 2. 3.

4. 5.

3210

3 3 3 3 3 3

3 3 3

3 3

3

3

4 5 6 7

Month Days above 908

May 4

June 7

July 14

August 12

September 8

Stem | Leaf

5 | 0 1 96 | 2 2 5 57 | 1 3 58 | 0 3 7 7 5 |0 5 50

Stem | Leaf

9 | 0 0 1 3 910 | 2 2 511 |12 | 0 3 3 8 8 9 9 |0 5 90

Stem | Leaf

2 | 4 7 73 | 1 2 6 6 6 94 | 05 | 8 8 9 2 |4 5 24

Stem | Leaf

9 | 4 6 8 9 910 | 0 1 2 4 8 911 | 2 212 | 0 1 9 |4 5

25 1 30}

2

24 1 36 1 21 1 30 1 21 1 30}}}}

6



NAME ______________________________________________ DATE ____________ PERIOD _____

2-52-5

ExampleExample

ExercisesExercises

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Skills Practice


NAME ______________________________________________ DATE ____________ PERIOD _____

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Use each set of data to make a line plot.

1. 59 39 50 60 45 39 59 45 31 59 2. 5 22 4 0 7 4 3 7 21 455 43 39 42 59 35 31 55 43 52 22 5 2 2 3 4 5 0 22 2

INCOME For Exercises 3–5, use the list that shows the income

from each assignment for a private investigator for a year.

3. Make a line plot of the data.

4. What was the median income per assignment for the investigator?

5. Does the median best represent the data?


6. 52 68 40 74 65 68 59 75 67 73 7. 1.5 2.3 1.7 3.0 4.1 5.3 4.755 63 39 42 59 35 31 59 63 42 1.9 2.2 2.8 4.3 5.2 4.1 2.2

EMPLOYMENT For Exercises 8–10, use the list

that shows the ages of employees at Watson &

Sterling Publications.

8. Make a stem-and-leaf plot of the data.

9. Which age occurs most frequently?

10. Does the mode best represent the data?Explain.

Stem | Leaf

||||

20 52 21 39 40 58 27 48 36 20 51 26

45 30 49 22 59 50 33 35 28 43 55 20

Stem | Leaf

|||||

Stem | Leaf

|||||

5000 5500 6000 6500 7000 7500 8000

3 3 3 3 3 33

3 3 3

3

3

6300 6100 7800

5600 7800 5100

6000 7200 6300

5100 6100 7800

765432102122

3 3 3 3 3 3 3 3

3 3 3 3 3 3

3 3 3

3

3

3

30 35 40 45 50 55 60

3 3 3 3 3 3 33 3 33

3 3 3 3 3

3 3

3

3

18


Use each set of data to make a line plot.

1. 72 47 62 78 49 67 80 2. 22 21.3 1.5 0.1 21.7 0.4 1.554 47 72 55 62 47 54 1 21.3 22 22.9 0.1 1.3 1.262 80 47 78 72 46 22.6 1.2 0.2 21.3 22.6

HEALTH For Exercises 3 and 4, use the list that shows the

grams of saturated fat in a serving of a variety of grains

such as bread, cereal, crackers, and pasta.

3. Make a line plot of the data.

4. Which measure of central tendency best describes the data? Explain.


5. 41 53 22 50 41 27 36 57 20 31 6. 4.1 7.3 6.9 5.7 4.8 7.3 5.628 52 41 33 28 27 41 52 22 30 6.0 4.4 7.5 4.6 7.9 5.1 7.7

EMPL0YMENT For Exercises 7–10, use the lists that show survey results of

students’ time spent on the Internet and on the telephone for a month.

7. Make a stem-and-leaf plot to compare the data.

8. Which value appears most frequently in each set of data?

9. Is the mode the best measure to compare the data?

10. Overall, did students spend more time on the Internet or the telephone?

Internet | Stem | Telephone

| || || || || || |

Internet Telephone

42 19 28 8 35 42 20 18 36 52 40 28 43 24 8 53

51 4 7 29 14 22 6 41 26 48 35 58 8 4

Stem | Leaf

||||

Stem | Leaf

||||

0 0.5 1 1.5 2 2.5 3

3

3

3

33

33

3

3

3 3 333

3

0.3 1.2 0.1 0.3 0.4

0.4 0.5 0.1 0.4 0.4

0.1 1.2 2.8 1.3 1.5

23 22.5 22 21.5 21 20.5 0 0.5 1 1.5

3 3

3

3

3

3 3

3

3

3 3

3

3 3

3

333

3

45 50 55 60 65 70 75 80

33

3

3

3

3 3

3

3

3

3

3

3 33

33

33

3

Practice


NAME ______________________________________________ DATE ____________ PERIOD _____

2-52-5

19

Reading to Learn Mathematics


NAME ______________________________________________ DATE ____________ PERIOD _____

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Pre-Activity How are line plots and averages used to make decisions?

Read the introduction to Lesson 2-5 at the top of page 88 in your textbook.

• What was the number one name for boys in all five decades?

• Look at the decade in which you were born. Is your name or the names ofany of the other students in your class in the top five for that decade?

Reading the Lesson

1. Use the line plot shown below to answer the questions.

a. What are the data points for the line plot?

b. What do the three 3’s above the 6 represent?

2. Explain what is meant by the frequency of a data number.

3. Use the stem-and-leaf plot shown at the right.

a. How is the number 758 represented on the plot?

b. Explain how you know there are 23 numbers in thedata.

Helping You Remember

4. Describe how you would explain the process of finding the median and mode from astem-and-leaf plot to a friend who missed Lesson 2-5.

Stem | Leaf

72 | 0 1 1 2 573 | 2 2 2 7 9 974 | 1 3 375 | 6 6 8 976 | 0 1 8 8 8 742 5 742

76543210212223242526

3 3 3 3 3 3 3 3 3 3 3 3 3 33 3 3 3 3 3 3 3

3 33

33

33

20


Runs Created

In The 1978 Bill James Baseball Abstract, the author introduced the “runs created” formula.

R 5 where for each player h 5 number of hits

w 5 number of walks,

t 5 number of total bases,

b 5 number of at-bats, and

R 5 approximate number of runs a team scores due to this player’s actions

1. As of June 29, 2001, Roberto Alomar of the Cleveland Indians and Seattle Marinersplayer Ichiro Suzuki were tied with the highest American League batting average at.351. Find the number of runs created by each player using the data below.

h w t b Runs Created

Alomar 97 37 145 276

Suzuki 121 13 159 345

Based on this information, who do you think is the more valuable American Leagueplayer? Why?

2. Carlos Lee of the Chicago White Sox and New York Yankee Bernie Williams were bothbatting .314. Find the number of runs created by each player using the data below.

h w t b Runs Created

Lee 81 13 141 258

Williams 74 31 123 236

3. Why would baseball teams want to calculate the number of runs created by each of theirplayers?

(h + w)t}(b + w)

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

2-52-5

21


Probability: Simple Probability and Odds

NAME ______________________________________________ DATE ____________ PERIOD _____

2-62-6


Less

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Probability The probability of a simple event is a ratio that tells how likely it is thatthe event will take place. It is the ratio of the number of favorable outcomes of the event tothe number of possible outcomes of the event. You can express the probability either as afraction, as a decimal, or as a percent.

Probability of a Simple Event For an event a, P(a) 5 .number of favorable outcomes}}}}number of possible outcomes

Mr. Babcock chooses

5 out of 25 students in his algebra class

at random for a special project. What is

the probability of being chosen?

P(being chosen) 5

The probability of being chosen is or .1}5

5}25

number of students chosen}}}}

total number of students

A bowl contains 3 pears,

4 bananas, and 2 apples. If you take a

piece of fruit at random, what is the

probability that it is not a banana?

There are 3 1 4 1 2 or 9 pieces of fruit.

There are 3 1 2 or 5 pieces of fruit that arenot bananas.

P(not banana) 5

5

The probability of not choosing a banana is .5}9

5}9

number of other pieces of fruit}}}}total number of pieces of fruit

Example 1Example 1 Example 2Example 2

ExercisesExercises

A card is selected at random from a standard deck of 52 cards. Determine each

probability.

1. P(10) 2. P(red 2) 3. P(king or queen)

4. P(black card) 5. P(ace of spades) 6. P(spade)

Two dice are rolled and their sum is recorded. Find each probability.

7. P(sum is 1) 8. P(sum is 6) 9. P(sum is less than 4)

10. P(sum is greater than 11) 11. P(sum is less than 15) 12. P(sum is greater than 8)

A bowl contains 4 red chips, 3 blue chips, and 8 green chips. You choose one chip

at random. Find each probability.

13. P(not a red chip) 14. P(red or blue chip) 15. P(not a green chip)

A number is selected at random from the list {1, 2, 3, …, 10}. Find each probability.

16. P(even number) 17. P(multiple of 3) 18. P(less than 4)

19. A computer randomly chooses a letter from the word COMPUTER. Find the probabilitythat the letter is a vowel.

22


Odds The odds of an event occurring is the ratio of the number of ways an event can occur(successes) to the number of ways the event cannot occur (failures).

Odds

A die is rolled. Find the odds of rolling a number

greater than 4.

The sample space is {1, 2, 3, 4, 5, 6}. Therefore, there are six possible outcomes. Since 5 and6 are the only numbers greater than 4, two outcomes are successes and four are failures.

So the odds of rolling a number greater than 4 is , or 1:2.

Find the odds of each outcome if the spinner at the right is

spun once.

1. multiple of 4 2. odd number

3. even or a 5 4. less than 4

5. even number greater than 5

Find the odds of each outcome if a computer randomly chooses a number between

1 and 20.

6. the number is less than 10 7. the number is a multiple of 4

8. the number is even 9. the number is a one-digit number

A bowl of money at a carnival contains 50 quarters, 75 dimes, 100 nickels, and

125 pennies. One coin is randomly selected.

10. Find the odds that a dime will not be chosen.

11. What are the odds of choosing a quarter if all the dimes are removed?

12. What are the odds of choosing a penny?

Suppose you drop a chip onto the grid at the right. Find the odds

of each outcome.

13. land on a shaded square

14. land on a square on the diagonal

15. land on square number 16

16. land on a number greater than 12

17. land on a multiple of 5

1

5

9

13

2

6

10

14

3

7

11

15

4

8

12

16

129

4

38

7

10

56

2}4

number of successes}}}number of failures



NAME ______________________________________________ DATE ____________ PERIOD _____

2-62-6

ExampleExample

ExercisesExercises

23

Skills Practice


NAME ______________________________________________ DATE ____________ PERIOD _____

2-62-6


Less

on

2-6

One chip is randomly selected from a jar containing 8 yellow chips, 10 blue chips,

7 green chips, and 5 red chips. Find each probability.

1. P(blue) 2. P(green)

3. P(yellow or green) 4. P(blue or yellow)

5. P(not red) 6. P(not blue)

Find the probability of each outcome if the spinner is spun once.

7. P(multiple of 3) 8. P(less than 7)

9. P(odd or 2) 10. P(not 1)

A person is born in the month of June. Find each probability.

11. P(date is a multiple of 6) 12. P(date is before June 15)

13. P(before June 7 or after June 24) 14. P(not after June 5)

Find the odds of each outcome if a computer randomly picks a letter in the name

The Petrified Forest.

15. the letter f 16. the letter e

17. the letter t 18. a vowel

CLASS SCHEDULES For Exercises 19–22, use the following information.

A student can select an elective class from the following: 3 in music, 5 in physical education,2 in journalism, 8 in computer programming, 4 in art, and 6 in drama. Find each of the oddsif a student forgets to choose an elective and the school assigns one at random.

19. The class is computer programming.

20. The class is drama.

21. The class is not physical education.

22. The class is not art.

18

45

6 3

7 2

24


One chip is randomly selected from a jar containing 13 blue chips, 8 yellow chips,

15 brown chips, and 6 green chips. Find each probability.

1. P(brown) 2. P(green)

3. P(blue or yellow) 4. P(not yellow)

A card is selected at random from a standard deck of 52 cards. Find each

probability.

5. P(heart) 6. P(black card)

7. P(jack) 8. P(red jack)

Two dice are rolled and their sum is recorded. Find each probability.

9. P(sum less than 6) 10. P(sum less than 2)

11. P(sum greater than 10) 12. P(sum greater than 9)

Find the odds of each outcome if a computer randomly picks a letter in the name

The Badlands of North Dakota.

13. the letter d 14. the letter a

15. the letter h 16. a consonant

CLASS PROJECTS For Exercises 17–20, use the following information.

Students in a biology class can choose a semester project from the following list: animalbehavior (4), cellular processes (2), ecology (6), health (7), and physiology (3). Find each ofthe odds if a student selects a topic at random.

17. the topic is ecology

18. the topic is animal behavior

19. the topic is not cellular processes

20. the topic is not health

SCHOOL ISSUES For Exercises 21 and 22, use the following information.

A news team surveyed students in grades 9–12 on whether to change the time school begins. One student will be selected atrandom to be interviewed on the evening news. The table gives the results.

21. What is the probability the student selected will be in the

9th grade?

22. What are the odds the student selected wants no change?

Grade 9 10 11 12

No change 6 2 5 3

Hour later 10 7 9 8

Practice


NAME ______________________________________________ DATE ____________ PERIOD _____

2-62-6

25

Reading to Learn Mathematics


NAME ______________________________________________ DATE ____________ PERIOD _____

2-62-6


Less

on

2-6

Pre-Activity Why is probability important in sports?

Read the introduction to Lesson 2-6 at the top of page 96 in your textbook.

Look up the definition of the word probability in a dictionary. Rewrite thedefinition in your own words.

Reading the Lesson

1. Write whether each statement is true or false. If false, replace the underlined word ornumber to make a true statement.

a. Probability can be written as a fraction, a decimal, or a percent.

b. The sample space of flipping one coin is heads or tails.

c. The probability of an impossible event is 1.

d. The odds against an event occurring are the odds that the event will occur.

2. Explain why the probability of an event cannot be greater than 1 while the odds of anevent can be greater than 1.

Helping You Remember

3. Probabilities are usually written as fractions, decimals, or percents. Odds are usuallywritten with a colon (for example, 1:3). How can the spelling of the word colon helpremember this?

26


Geometric Probability

If a dart, thrown at random, hits the triangular board shown at the right, what is the probability that it will hit the shaded region? Thiscan be determined by comparing the area of the shaded region to thearea of the entire board. This ratio indicates what fraction of the tosses should hit in the shaded region.

5

5 or

In general, if S is a subregion of some region R, then the probability, P(S), that a point,chosen at random, belongs to subregion S is given by the following:

P(S) 5

Find the probability that a point, chosen at random, belongs to the shaded

subregions of the following figures.

1. 2. 3.

4. 5. 6.

7. 8. 9.2

2

4 48

4

4

4

4 4

6

6

66

66

6Ï·3 6Ï·3

5

5

55 55

6

6

4

4

4 4

4

6

4

4 4

6 63 3

5

5

area of subregion S}}}

area or region R

1}2

12}24

}1

2}(4)(6)}

}1

2}(8)(6)

area of shaded region}}}area of triangular board

6

44

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

2-62-6

27

Documents

Algebra 1A Unit 05...Unit 05 Sections 1.9, 2.5, 2.6 GUIDED NOTES NAME _____ Teacher _____ Period _____ 1. Section 1-9: Analyzing Tables and Graphs Why are graphs used to display data?

Algebra 1A Unit 05...Unit 05 Sections 1.9, 2.5, 2.6 GUIDED NOTES NAME ___ Teacher _ Period ___ 1. Section 1-9: Analyzing Tables and Graphs Why are graphs used to display data?