7th grade - njctlcontent.njctl.org/courses/math/7th-grade/statistics... · 2015. 11. 19. · of...

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7th Grade Statistics and Probability

20151119

www.njctl.org

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Table of Contents

• Introduction to Probability• Experimental and Theoretical

• Word Problems• Probability of Compound Events

Click on a topic to go to that section.

• Sampling

• Measures of Center• Measures of Variation• Mean Absolute Deviation• Glossary

Teacher N

otes Vocabulary Words are bolded

in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.

4

Introduction toProbability

Click to go to Table of Contents

5

One way to express probability is to use a fraction.

Number of favorable outcomes

Total number of possible outcomes

Probability of an event

=

P(event)

Probability

6

Example: What is the probability of flipping a nickel and the nickel landing on heads?

Step 1: What are the possible outcomes?

Step 2: What is the number of favorable outcomes?

Step 3: Put it all together to answer the question.The probability of flipping a nickel and landing on heads is: 1 2

click

click

click

Answer

Probability

7

Probability can be expressed in many forms. For example, the probability of flipping a head can be expressed as:

1 or 50% or 1:2 or 0.5 2

The probability of randomly selecting a blue marble can be expressed as:

1 or 1:6 or 16.7% or .167 6

Probability

8

When there is no chance of an event occurring, the probability of the event is zero (0).

When it is certain that an event will occur, the probability of the event is one (1).

0 14

12

34

1

Impossible

Unlikely

Equally Likely

Likely

Certain

The less likely it is for an event to occur, the probability is closer to 0 (i.e. smaller fraction).

The more likely it is for an event to occur, the probability is closer to 1 (i.e. larger fraction).

Probability

9

Without counting, can you determine if the probability of picking a red marble is lesser or greater than 1/2?

It is very likely you will pick a red marble, so the probability is greater than 1/2 (or 50% or 0.5)

Click to Reveal

What is the probability of picking a red marble? 56Clickto

Reveal

Add the probabilities of both events. What is the sum?

1 + 5 = 16 6

Click to Reveal

Probability

10

Note:The sum of all possible outcomes is always equal to 1.

There are three choices of jelly beans grape, cherry and orange. If the probability of getting a grape is 3/10 and the probability of getting cherry is 1/5, what is the probability of getting orange?

3 + 1 + ? = 110 5 ?

5 + ? = 110 ?

The probability of getting an orange jelly bean is 5 . 10

Probability

11

1 Arthur wrote each letter of his name on a separate card and put the cards in a bag. What is the probability of drawing an A from the bag?

A 0B 1/6C 1/2D 1

A R T H U R

Probability = Number of favorable outcomes Total number of possible outcomesClick for hint

Answer

B

12

2 Arthur wrote each letter of his name on a separate card and put the cards in a bag. What is the probability of drawing an R from the bag?

A 0B 1/6C 1/3D 1

A R T H U R

Probability = Number of favorable outcomes Total number of possible outcomes

A

Click for hint

Answer

C

13

3 Matt's teacher puts 5 red, 10 black, and 5 green markers in a bag. What is the probability of Matt drawing a red marker?

A 0

B 1/4

C 1/10

D 10/20

Probability = Number of favorable outcomes Total number of possible outcomes

Click for hint

Answer

B

14

4 What is the probability of rolling a 5 on a fair number cube?

Answer

1/6

15

5 What is the probability of rolling a composite number on a fair number cube?

Answer

1/3

16

6 What is the probability of rolling a 7 on a fair number cube?

Answer

0

17

7 You have black, blue, and white tshirts in your closet. If the probability of picking a black tshirt is 1/3 and the probability of picking a blue tshirt is 1/2, what is the probability of picking a white tshirt?

Answer

1/6

18

8 If you enter an online contest 4 times and at the time of drawing its announced there were 100 total entries, what are your chances of winning?

Answer

1/25

19

9 Mary chooses an integer at random from 1 to 6. What is the probability that the integer she chooses is a prime number?

A

B

C

D

From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.

Answer

B

20

10 Each of the hats shown below has colored marbles placed inside. Hat A contains five green marbles and four red marbles. Hat B contains six blue marbles and five red marbles. Hat C contains five green marbles and five blue marbles. If a student were to randomly pick one marble from each of these three hats, determine from which hat the student would most likely pick a green marble. Justify your answer.

A Hat

B Hat

C Hat

From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011

Answer

21

Determine the fewest number of marbles, if any, and the color of these marbles that could be added to each hat so that the probability of picking a green marble will be onehalf in each of the three hats.Hat A contains five green marbles and four red marbles. Hat B contains six blue marbles and five red marbles. Hat C contains five green marbles and five blue marbles.


Answer

Hat A needs 1 red marble.

Hat B needs 11 green marbles.

Hat C does not need marbles.

22

Experimental &

TheoreticalProbability


23

Click on an object. What is the outcome?Outcomes

24

number of times the outcome happened number of times experiment was repeated

Experimental Probability

Flip the coin 5 times and determine the experimental probability of heads.


Heads Tails

Answer

25

Example 1 GolfA golf course offers a free game to golfers who make a holeinone on the last hole. Last week, 24 out of 124 golfers achieved this. Find the experimental probability that a golfer makes a holeinone on the last hole.

Out of 31 golfers, you could expect 6 to make a holeinone on the last hole. Or there is a 19% chance of a golfer making a holeinone on the last hole.


P(holeinone) = # of successes # of trials

= 24 124

= 6 31

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Example 2 SurveysOf the first 40 visitors through the turnstiles at an amusement park, 8 visitors agreed to participate in a survey being conducted by park employees. Find the experimental probability that an amusement park visitor will participate in the survey.

You could expect 1 out of every 5 people to participate in the survey. Or there is a 20% chance of a visitor participating in the survey.


P(participation) = # of successes # of trials

= 8 40

= 1 5

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# on Die Picture of Roll Results 1 1 one 2 3 twos 3 1 three 4 0 fours 5 4 fives 6 1 six

Sally rolled a die 10 times and the results are shown below.

Use this information to answer the following questions.


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11 What is the experimental probability of rolling a 5?

A 1/2

B 5/4

C 4/5

D 2/5

# on Die Picture of Roll Results 1 1 one

2 3 twos

3 1 three

4 0 fours

5 4 fives

6 1 six

These are the results after 10 rolls of the die

Answer

D

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12 What is the experimental probability of rolling a 4?

A 1/2

B 5/4

C 0

D 4/4


2 3 twos

3 1 three

4 0 fours

5 4 fives

6 1 six


Answer

C

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13 Based on the experimental probability you found, if you rolled the die 100 times, how many sixes would you expect to get? A 6 sizes

B 10 sixes

C 12 sixes

D 60 sixes


Answer

B


2 3 twos

3 1 three

4 0 fours

5 4 fives

6 1 six

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14 Mike flipped a coin 15 times and it landed on tails 11 times. What is the experimental probability of landing on heads?

Answer

4/15

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Theoretical Probability

What is the theoretical probability of spinning green?

Answer

1/4

Is this a fair probability?

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number of favorable outcomestotal number of possible outcomes

34


Example 1 MarblesFind the theoretical probability of randomly choosing a white marble from the marbles shown.

There is a 2 in 5 chance of picking a white marble or a 40% possibility.

P(white) = # of favorable outcomes # of possible outcomes

4 2 10 5

==

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Theoretical ProbabilityExample 2 MarblesSuppose you randomly choose a gray marble. Find the probability of this event.

There is a 3 in 10 chance of picking a gray marble or a 30% possibility.

P(gray) = # of favorable outcomes # of possible outcomes

3 10

=

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There is a 1 in 2 chance of getting tails when you flip a coin or a 50% possibility.

Theoretical ProbabilityExample 3 CoinsFind the probability of getting tails when you flip a coin.

P(tails) = # of favorable outcomes # of possible outcomes

1 2

=

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15 What is the theoretical probability of picking a green marble?

A 1/8

B 7/8

C 1/7

D 1

R

R

G

W

W

Y

Y

B

Answer

A

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16 What is the theoretical probability of picking a black marble?

A 1/8

B 7/8

C 1/7

D 0

R

R

G

W

W

Y

Y

B Answer

D

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17 What is the theoretical probability of picking a white marble?

A 1/8

B 7/8

C 1/4

D 1

R

R

G

W

W

Y

Y

B Answer

C

40

18 What is the theoretical probability of not picking a white marble?

A 3/4

B 7/8

C 1/7

D 1

R

R

G

W

W

YY

B

Answer

A

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19 What is the theoretical probability of rolling a three?

A 1/2B 3C 1/6D 1

Answer

C

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20 What is the theoretical probability of rolling an odd number? A 1/2B 3C 1/6D 5/6 A

nswer

A

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21 What is the theoretical probability of rolling a number less than 5?A 2/3B 4C 1/6D 5/6

Answer

A

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22 What is the theoretical probability of not rolling a 2?

A 2/3B 2C 1/6D 5/6

Answer

D

45

23 Seth tossed a fair coin five times and got five heads. The probability that the next toss will be a tail is

A 0

B

C

D


Answer

46

24 Which inequality represents the probability, x, of any event happening?

A x ≥ 0B 0 < x < 1C x < 1D 0 ≤ x ≤ 1


Answer

D

47

25 The spinner shown is divided into 8 equal sections.

The arrow on this spinner is spun once.

What is the probability that the arrow will land on a section labeled with a number greater than 3?

Enter only your fraction.

From PARCC EOY sample test calculator #1

Answer

http://practice.parcc.testnav.com/#

48

26 Reagan will use a random number generator 1,200 times. Each result will be a digit form 1 to 6. Which statement best predicts how many times the digit 5 will appear among the 1,200 results?

A It will appear exactly 200 times.

B It will appear close to 200 times but probably not exactly 200 times.

C It will appear exactly 240 times.

D It will appear close to 240 times but probably not exactly 240 times.


Answer


49

Class Activity• Each student flips a coin 10 times and records the number of heads and the number of tail outcomes.

• Each student calculates the experimental probability of flipping a tail and flipping a head.

• Use the experimental probabilities determined by each student to calculate the entire class's experimental probability for flipping a head and flipping a tail.

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Answer the following:

What is the theoretical probability for flipping a tail? A head?

Compare the experimental probability to the theoretical probability for 10 experiments.

Compare the experimental probability to the theoretical probability when the experiments for all of the students are considered?

Class Activity

51

Sampling

Return to Table of Contents

52

Your task is to count the number of whales in the ocean or the number of squirrels in a park.

How could you do this?

What problems might you face?

A sample is used to make a prediction about an event or gain information about a population.

A whole group is called a POPULATION.

A part of a group is called a SAMPLE.

Sampling

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A sample is considered

Example: To find out how many people in New York feel about mass transit, people at a train station are asked their opinion. Is this situation representative of the general population?

Sampling

random (or unbiased) when every possible sample of the same size has an equal chance of being selected. If a sample is biased, then information obtained from it may not be reliable.

Answer

54

Determine whether the situation would produce a random sample.

You want to find out about music preferences of people living in your area. You and your friends survey every tenth person who enters the mall nearest you.

Sampling

Answer

55

27 Food services at your school wants to increase the number of students who eat hot lunch in the cafeteria. They conduct a survey by asking the first 20 students that enter the cafeteria lunch line to determine the students' preferences for hot lunch. Is this survey reliable? Explain your answer.

Yes No

Answer

56

28 The guidance counselors want to organize a career day. They will survey all students whose ID numbers end in a 7 about their grades and career counseling needs. Would this situation produce a random sample? Explain your answer.Yes No A

nswer

Yes

57

29 The local newspaper wants to run an article about reading habits in your town. They conduct a survey by asking people in the town library about the number of magazines to which they subscribe. Would this produce a random sample? Explain your answer.

Yes No

Answer

No

58

How would you estimate the size of a crowd?What methods would you use?

Could you use the same methods to estimate the number of wolves on a mountain?

Sampling

59

A whole group is called a population.

A part of a group is called a SAMPLE.

When biologists study a group of wolves, they are choosing a sample . The population is all the wolves on the mountain.

Population

Sample

Sampling

60

Suppose this represents all the wolves on the mountain.

One way to estimate the number of wolves on a mountain is to use the capturerecapture method.

Sampling

61

Wildlife biologists first find some wolves and tag them.

CaptureRecapture Method

62

Then they release them back onto the mountain.


63

They wait until all the wolves have mixed together.Then they find a second group of wolves and count how many are tagged.


64

Biologists use a proportion to estimate the total number of wolves on the mountain:

tagged wolves on mountain tagged wolves in second group total wolves on mountain total wolves in second group

For accuracy, they will often conduct more than one recapture.

=

8 2 w 9

2w = 72 w = 36

=

There are 36 wolves on the mountain


65

Try This:Biologists are trying to determine how many fish are in the Rancocas Creek. They capture 27 fish, tag them and release them back into the Creek. 3 weeks later, they catch 45 fish. 7 of them are tagged. How many fish are in the creek?

27 7 f 45

27(45) = 7f1215 = 7f173.57 = f

=

There are 174 fish in the river


66

Try This:

315 out of 600 people surveyed voted for Candidate A. How many votes can Candidate A expect in a town with a population of 1500?

Answer


67

30 Eight hundred sixty out of 4,000 people surveyed watched Dancing with the Stars. How many people in the US watched if there are 93.1 million people?

Answer

68

31 Six out of 150 tires need to be realigned. How many out of 12,000 are going to need to be realigned?

Answer

69

32 You are an inspector. You find 3 faulty bulbs out of 50. Estimate the number of faulty bulbs in a lot of 2,000.

Answer

120 faulty bulbs

70

33 You survey 83 people leaving a voting site. 15 of them voted for Candidate A. If 3,000 people live in town, how many votes should Candidate A expect?

Answer

about 542 votes

71

34 The chart shows the number of people wearing different types of shoes in Mr. Thomas' English class. Suppose that there are 300 students in the cafeteria. Predict how many would be wearing hightop sneakers. Explain your reasoning.

Number of Students

Lowtop sneakers 12

Hightop sneakers 7

Sandals 3

Boots 6

Shoes

Answer

75 students

72

35 Josephine owns a diner that is open every day for breakfast, lunch, and dinner. She offers a regular menu and a menu with specials for each of the three meals. She wanted to estimate the percentage of her customers that order form the menu with specials. She selected a random sample of 50 customers who had lunch at her diner during a threemonth period. She determined that 28% of these people ordered for the menu with specials.

Which statement about Josephine's sample is true?

A The sample is the percentage of customers who order from the menu with specials.

B The sample might not be representative of the popultation because it only included lunch customers.

C The sample shows that exactly 28% of Josephine's customers order from the menu with specials.

D No generalizations can be made from this sample, because the sample size of 50 is too small. From PARCC EOY sample test

calculator #13

Answer


73

Multiple SamplesThe student council wanted to determine which lunch was the most popular among their students. They conducted surveys on two random samples of 100 students. Make at least two inferences based on the results.

Student Sample Hamburgers Tacos Pizza Total#1 12 14 74 100

#2 12 11 77 100

• Most students prefer pizza.• More people prefer pizza than hamburgers and tacos combined.

74

Try This!

The NJ DOT (Department of Transportation) used two random samples to collect information about NJ drivers. The table below shows what type of vehicles were being driven. Make at least two inferences based on the results of the data.

Driver Sample Cars SUVs Mini Vans Motorcycles Total

#1 37 43 12 8 100#2 33 46 11 10 100

Multiple Samples

Answer

• SUV's are the most popular vehicles among NJ drivers.• Cars are the second most popular vehicles among NJ drivers.• SUV's are at least twice as popular as mini vans and motorcycles combined.

75

The student council would like to sell potato chips at the next basketball game to raise money. They surveyed some students to figure out how many packages of each type of potato chip they would need to buy. For home games, the expected attendance is approximately 250 spectators. Use the chart to answer the next three questions.

Student Sample Regular BBQ Cheddar

#1 8 10 7#2 8 11 6

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36 How many students participated in each survey?


#1 8 10 7#2 8 11 6

Answer

25

77

37 According to the two random samples, which flavor potato chip should the student council purchase the most of?

A RegularB BBQC Cheddar


#1 8 10 7#2 8 11 6

Answer

B

78

38 Use the first random sample to evaluate the number of packages of cheddar potato chips the student council should purchase.


#1 8 10 7#2 8 11 6

Answer

70

79

Word Problems


80

19 shots made 100 shots attempted

= 19%

Example 1 SoccerErica loves soccer! The ladies' coach tells Erica that she scored 19% of her attempts on goal last season. This season, the coach predicts the same percentage for Erica. Erica reports she attempted approximately 1,100 shots on goal last season. Her coach suggests they estimate the number of goals using experimental probability. What do you know about percentages to figure out the relationship of goals scored to goals attempted?

Experimental Probability =number of times the outcome happened number of times experiment was repeated

number of goals

number of attempts Erica's Experimental Probability

=Move to Reveal

Move to Reveal

click to reveal

Word Problem

81

19 100

20 100

is very close to

so she makes about 20% of her shots on goal.

Let's estimate the number of goals Erica scored.

1,100 is very close to 1,000. So we will estimate that Erica has about 1,000 attempts

About what percent would be a good estimate to use?

About how many attempts did Erica take?

Erica makes 19% of her shots on goal.

Erica takes 1,100 shots on goal.

clickclick

Word Problem

82

Erica figures she made about 200 of her shots on goal.

Erica wants to find 20% of 1,000. Her math looks like this:

click to reveal

Word Problem

83

What are the actual values that will give you 19%?Cha

llenge

Remember sometimes it helps to turn a percent into a decimal prior to solving the problem.Click for hint

Word Problem

Answer

84

Example 2 GardeningLast year, Lexi planted 12 tulip bulbs, but only 10 of them bloomed. This year she intends to plant 60 tulip bulbs. Use experimental probability to predict how many bulbs will bloom.

Based on her experience last year,Lexi can expect 50 out of 60 tulips to bloom.

Solve this proportion by equivalent fractions.


10 bloom 12 total

x bloom60 total

=

10 bloom 12 total

50 bloom 60 total

=

85

Example 3 BasketballToday you attempted 50 free throws and made32 of them. Use experimental probability to predict how many free throws you will make tomorrow if you attempt 75 free throws.

Based on your performance yesterday,you can expect to make 48 free throws out of 75 attempts.

Solve this proportion using cross products.


32 75 = 50 x

2400 = 50x

48 = x

32 made 50 attempts

x made 75 attempts

=

86

Number of attempts Number of goals


100

1000

500

2000

30

600

150

1600

Now, its your turn. Calculate the experimental probability for the number of goals.


87

39 Tom was at bat 50 times and hit the ball 10 times. What is the experimental probability for hitting the ball?

Answer

88

40 Tom was at bat 50 times and hit the ball 10 times. Estimate the number of balls Tom hit if he was at bat 250 times.

Answer

50

89

41 What is the theoretical probability of randomly selecting a jack from a deck of cards?

Answer

1/13

90

42 Mark rolled a 3 on a die for 7 out of 20 rolls. What is the experimental probability for rolling a 3?

Answer

91

43 Mark rolled a 3 on a die for 7 out of 20 rolls. What is the theoretical probability for rolling a 3?

Answer

92

44 Some books are laid on a desk. Two are English, three are mathematics, one is French, and four are social studies. Theresa selects an English book and Isabelle then selects a social studies book. Both girls take their selections to the library to read. If Truman then selects a book at random, what is the probability that he selects an English book?

Answer

1/8

93

45 What is the probability of drawing a king or an ace from a standard deck of cards?

A 2/52B 4/52C 2/13D 8/52 A

nswer

C

94

46 What is the probability of drawing a five or a diamond from a standard deck of cards?

A 4/13B 13/52C 2/13D 16/52

Answer

A

95

Lindsey would like to know the number of people at a movie theater that will buy a movie ticket and popcorn. Based on past data, the probability that a person who is selected at random from those that buy movie tickets and also buy popcorn is 0.6. Lindsey designs a simulation to estimate the probability that exactly two in a group of three people selected randomly at a movie theater will buy both a movie ticket and popcorn. For the simulation Lindsey used a number generator that generates random numbers.

• Any number from 1 through 6 represents a person who buys a movie ticket and popcorn.

• Any number from 7 through 9 or 0 represents a person who buys only a movie ticket.

• Use info for next two questions.



96

47 Part A In the simulation, one result was "100". What does this result simulate?

A No one in a group of three randomlychosen people who buy movie tickets also buys popcorn.

B Exactly one person in a group of three randomlychosen people who buy movie tickets also buys popcorn.

C Exactly two people in a group of three randomlychosen people who buy movie tickets also buy popcorn.

D All three people in a group of three randomlychosen people who buy movie tickets also buy popcorn.

Answer

97

48 Part B

Use the results of the simulation to estimate the probability that exactly two of three people selected at random from those who buy movie tickets will also buy popcorn.

Answer

98

Probability of Compound Events


99

Probability of Compound Events

For the probability of compound events, first decide if the two events are independent or dependent.

When the outcome of one event does not affect the outcome of another event, the two events are independent.

Use formula:Probability (A and B) = Probability (A) Probability (B)

100

Independent ExampleSelect a card from a deck of cards, replace it in the deck, shuffle the deck, and select a second card.

What is the probability that you will pick a 6 and then a king?

P (6 and a king) = P(6) P(king) 4 4 = 1 52 52 169

101

When the outcome of one event affects the outcome of another event, the two events are dependent.

Use formula:

Probability (A & B) = Probability(A) Probability(B given A)

Dependent Events

102

Select a card from a deck of cards, do not replace it in the deck, shuffle the deck, and select a second card.

What is the probability that you will pick a 6 and then a king?

Dependent Example

P (6 and a king) = P(6) P(king given a six has been selected) 4 4 = 4 52 51 663

Notice your demominator when down by 1. Why?

103

Independent Dependent

Try to name some other independent and dependent events.

Independent & Dependent Examples

104

49 The names of 6 boys and 10 girls from your class are put in a hat. What is the probability that the first two names chosen will both be boys? (w/o replacement)

Answer

105

50 A lottery machine generates numbers randomly. Two numbers between 1 and 9 are generated. What is the probability that both numbers are 5?

Answer

106

51 The TV repair person is in a room with 20 broken TVs. Two sets have broken wires and 5 sets have a faulty computer chip. What is the probability that the first TV repaired has both problems?

Answer

107

52 What is the probability that the first two cards drawn from a full deck are both hearts? (without replacement)

Answer

108

53 A spinner containing 5 colors: red, blue, yellow, white and green is spun and a die, numbered 1 through 6, is rolled. What is the probability of spinning green and rolling a two?

Answer

109

54 A drawer contains 5 brown socks, 6 black socks, and 9 navy blue socks. The power is out. What is the probability that Sam chooses two socks that are both black?

Answer

110

55 At a school fair, the spinner represented in the accompanying diagram is spun twice.

What is the probability that it will land in section G the first time and then in section B the second time?

A

B

C

D

R G

B


Answer

111

56 A student council has seven officers, of which five are girls and two are boys. If two officers are chosen at random to attend a meeting with the principal, what is the probability that the first officer chosen is a girl and the second is a boy?

A

B

C

D


Answer

112

57 The probability that it will snow on Sunday is .

The probability that it will snow on both Sunday and Monday is .

What is the probability that it will snow on Monday, if it snowed on Sunday?

A

B 2

C

D


Answer

113

Measures of Center


114

Sometimes we can make general statements about a set of data as shown in this first question.

Generalizations

115

58 Alexis chose a random sample of 10 jars of almonds from each of two different brands, X and Y. Each jar in the sample was the same size. She counted the number of almonds in each jar. Her results are shown in the plots.

A The number of almonds in jars from Brand X tends to be greater and more consistent than those from Brand Y.

B The number of almonds in jars from Brand X tends to be greater and less consistent than those from Brand Y.

C The number of almonds in jars from Brand X tends to be fewer and more consistent than those from Brand Y.

D The number of almonds in jars from Brand X tends to be fewer and less consistent than those from Brand Y.


Answer


116

Other times we will make statements about the data based on measure of center and variation that we can calculate. This will be the topics for the rest of

this chapter.

Generalizations

117

Measures of Center Vocabulary Review

Median The middle data value when the values are written in numerical order

Mean (Average) The sum of the data values divided by the number of items

Mode The data value that occurs the most often

118

Measures of Center

Joey wanted to convince his mom to give him some money for a snack from the concession stand. Below are the prices of the different snacks.

$1.75, $0.75, $1.25, $0.75, $2.50, $2.00

119

What is the mean of this data set?$1.75, $0.75, $1.25, $0.75, $2.50, $2.00

Step 1: Add up all of the numbers.1.75 + 0.75 + 1.25 + 0.75 + 2.50 + 2.00 = 9.00

Step 2: Divide the sum by the number of items listed.9.00 / 6 = 1.50

The mean cost of concession stand snacks is $1.50.

Mean Example

120

Find the mini mean

1.25 + 1.75 = 1.50

2

What do you do when you have two numbers left? (click)

What is the median of this data set?$1.75, $0.75, $1.25, $0.75, $2.50, $2.00

Step 1: Order the numbers from least to greatest.0.75, 0.75, 1.25, 1.75, 2.00, 2.50

Step 2: Find the middle value.0.75, 0.75, 1.25, 1.75, 2.00, 2.50

The median cost of concession stand snacks is $1.50.

Median Example

121

What is the mode of this data set?$1.75, $0.75, $1.25, $0.75, $2.50, $2.00

Step 1: Look for the number that appears most often.1.75, 0.75, 1.25, 0.75, 2.50, 2.00

The mode cost of concession stand snacks is $0.75.

Mode Example

122

Mean

$1.50

Median

$1.50

Mode

$0.75

How can Joey use this information to ask his mom for money?$1.75, $0.75, $1.25, $0.75, $2.50, $2.00

Measures of Center

123

Time Spent Texting Daily by

7th Grade Students

(in minutes)

600 15 30 45 75 90 105 120

Girls

600 15 30 45 75 90 105 120

Boys

Measures of Center

Use the dot plots to compare the 2 samples.

124

600 15 30 45 75 90 105 120

Girls

Find the mean, median, and mode for the sample of girls.

Measures of Center

Answer

125

600 15 30 45 75 90 105 120

Boys

Measures of Center

Find the mean, median, and mode for the sample of boys.

Answer

126

Girls BoysMean 88.5 40.5Median 90 30Mode 60 30 and 60

Measures of Center

Now compare the two measures of center.

Make a statement about the average time spent texting daily by 7th grade students.

Answer

127

59 What is the mean of the stemandleaf plot?

Stem Leaf

1 1 1 22 0 0 3

5 54 8

Key: 1 | 1 = 11 Answer

25

128

60 What is the median of the stemandleaf plot?

Stem Leaf

1 1 1 22 0 0 3

5 54 8

Key: 1 | 1 = 11

Answer

20

129

61 What is the mode of the stemandleaf plot?

Stem Leaf

1 1 1 22 0 0 3

5 54 8

Key: 1 | 1 = 11

Answer

11 and 20

130

62 What is the mean of the stemandleaf plot?

Stem Leaf

1 8 93 7 7 9

Key: 1 | 8 = 1.8

Answer

3

131

63 What is the median of the stemandleaf plot?

Stem Leaf

1 8 93 7 7 9

Key: 1 | 8 = 1.8 Answer

3.7

132

64 What is the mode of the stemandleaf plot?

Stem Leaf

1 8 93 7 7 9

Key: 1 | 8 = 1.8

Answer

3.7

133

Miss M's Math Class Scores

9050 60 70 80 100

1st Period Scores

Measures of CenterUse the dot plots to find the measures of center.

Answer

134

Miss M's Math Class Scores

9050 60 70 80 100

8th Period Scores

Measures of CenterUse the dot plots to find the measures of center.

Answer

135

Measures of Center

Write a statement comparing the averages of Miss M's 1st period class scores to her 8th period class scores.

136

Measures of Variation


137

Measures of Variation Vocabulary Review

Quartiles are the values that divide the data in four equal parts.

Lower (1st) Quartile (Q1) The median of the lower half of the data.

Upper (3rd) Quartile (Q3) The median of the upper half of the data.

Interquartile Range The difference of the upper quartile and the lower quartile. (Q3 Q1)

Range The difference between the greatest data value and the least data value.

138

1, 5, 8, 3, 2, 5, 2, 8, 9, 5

1, 2, 2, 3, 5, 5, 5, 8, 8, 9

• To find the interquartile range of the data set, we first have to find the quartiles.

Step 1 : Order the numbers from least to greatest.

Interquartile Range

139

1, 2, 2, 3, 5, 5, 5, 8, 8, 9

Step 2 : Find the median.

5median

*Note :

• If the median falls in between two data values, all of the values are still used to calculate the upper and lower quartiles.

• If the median falls exactly on one of the two data values, than that values is NOT used to calculate the upper and lower quartiles.

Interquartile Range

140

1, 2, 2, 3, 5, 5, 5, 8, 8, 9

5median

8Upper

2Lower

Quartile Quartile

Step 3 : Find the upper and lower quartiles.

Find the mean of each half of the data set.

Interquartile Range

141

Upper LowerQuartile Quartile

Step 4 : Subtract the lower quartile from the upper quartile.

Interquartile= Range

8 2 = 6

Interquartile Range

142

1, 2, 2, 3, 5, 5, 5, 8, 8, 9

• To find the range, subtract the least value from the greatest value.

Greatest LeastValue Value = Range

9 1 = 8

Sample Range

143

1, 2, 2, 3, 5, 5, 5, 8, 8, 9

5Median

8Upper

2Lower

Quartile Quartile

1Least Value

9Greatest Value

BoxandWhisker Plot

These 5 values are used to create a boxandwhisker plot. To do this, plot all 5 values on the number line and then connect them to look like a box with whiskers on both sides. click just above the number line to reveal

10 2 3 4 5 6 7 8 9 10

144

65 What is the median of the data set?

10 2 3 4 5 6 7 8 9 10

Answer

4

145

66 What is the interquartile range using the given information?

Least Value = 3

Lower Quartile = 6

Median = 7

Upper Quartile = 10

Greatest Value = 11

Answer

4

146

67 What is the range for the following data set?

3, 5, 10, 4, 2, 2, 1

Answer

9

147

68 What is the interquartile range for the following data set?

3, 5, 10, 4, 2, 2, 1

Answer

3

148

Mean Absolute Deviation


149

Mean absolute deviation the average distance between each data value and the mean.

Mean Absolute Deviation Vocabulary

150


Find the mean absolute deviation of the following data.

Quiz Scores

65, 75, 90, 90, 100

Step 1: Find the mean.

65 + 75 + 90 + 90 + 100 = 420 = 84 5 5

151

Score Deviation from mean

Absolute deviation from

mean65 65 84 = 19 |19| = 1975 75 84 = 9 |9| = 990 90 84 = 6 |6| = 690 90 84 = 6 |6| = 6100 100 84 = 16 |16| = 16

Step 2: Find the absolute deviation. To do this you need to subtract the mean and each data point. Then take the absolute value of each difference.


152

Absolute deviation from mean

|19| = 19|9| = 9|6| = 6|6| = 6|16| = 16

Mean Absolute DeviationStep 3: Find the mean absolute deviation (MAD). To do this find the mean using the absolute deviation numbers.

19 + 9 + 6 + 6 + 16 5

= 56 = 11.2 5

The MAD is

11.2 points.

Answer This means that the average

test score is 11.2 points from the mean of 84.

153

5 6 4 32 1 7 8 9 10 5 6 4 32 1 7 8 9 10

Girls' Team Boys' Team

Comparing Two Data SetsThe number of goals scored by the players on the boys' and girls' LAX teams are displayed below.

Compare the variability of the mean goals scored for both teams.

154

5 6 4 32 1 7 8 9 10

Girls' Team

5 6 4 32 1 7 8 9 10

Boys' Team

Comparing Two Data Sets

Step 1: Find the mean for each team.

Answer

155

Goals Mean Deviation Absolute Mean Dev. Goals Mean Deviation Absolute

Mean Dev.


Comparing Two Data SetsStep 2: Find the absolute deviations.

156



Step 3: Find the mean absolute deviations.

Answer

2 + 2 + 1 + 0 + 0 + 0 + 0 + 5

157


Comparison Statements1.25 = 1.25

The variability is equal for both the boys and girls LAX teams.

On average, the boy players scored 1 more goal than the girl players. (How do you know this?)

Answer

158

Pages per Chapter in Hunger Games

10 15 20 25 30

x

xxxx

xxx

xxxxxxx

xxx

xxxx x

xxx x

10 15 20 25 30

xxxxx

xx

xx

xx

xx x

xx x

xxx

xx

Pages per Chapter in Twilight

Use the following data to answer the next seven questions.


159

69 What is the mean number of pages per chapter in the Hunger Games?

Answer

13.63 pages

160

70 What is the mean number of pages per chapter in Twilight?

Answer

20.41 pages

161

71 What is the difference of the means?

Answer

6.78

162

72 What is the mean absolute deviation of the data set for Hunger Games?

(Hint: Round mean to the nearest ones.)

Answer

1.78

163

73 What is the mean absolute deviation of the data set for Twilight?

(Hint: Round mean to the nearest ones.)

Answer

4.32

164

74 Which book has more variability in the number of pages per chapter?

A Hunger GamesB Twilight

Answer

B

165

75 On average, there are ______ pages per chapter in the Hunger Games than in Twilight.

A more

B less

Answer

B less

166

Glossary

Return toTable ofContents

Teacher N

otes Vocabulary Words are bolded

in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.

167

Back to Instruction

Biased SampleWhen every possible sample of the same size does not have an equal chance of being selected.

Asking only flight attendants if they believe flying is safe.

Asking everyone in Hershey Park

if they like chocolate.

Asking everyone at ComicCon if they like comic

books.

168

Back to Instruction

CaptureRecapture MethodA method of sampling that is used to try and estimate the entire population. A sample of animals are caught, tagged, and then released into the wild. Later a second sample of animals are

caught to compute using a ratio the amount of tagged animals to the population as a whole.

169

Back to Instruction

Compound Event

A combination of two or more simple events.

The prob. of flipping heads

AND rolling 4 on a die.

The prob. of selecting a Jack OR a 3 card.

The prob. of selecting a Jack AND a 3 card.

170

Back to Instruction

Dependent Event

When the outcome of one affects the outcome of another event.

Probability (A & B) = Prob(A) *Prob(B given A)

The prob. of selecting a Jack AND a 3 card.

171

Back to Instruction

Equally Likely

When all the outcomes have the same chance of occurring.

Sides on a Coin

A Fair Die A Fair Spinner

172

Back to Instruction


The ratio of the number of times an event occurs to the total number of times that the activity is performed.

number of times the outcome happened number of times experiment was repeated


Last week, 24 out of 124 golfers hit a holeinone on the last hole. Find the experimental

probability that a golfer makes this

shot.

P(holeinone) =

# of successes = # of trials

24 124 = 6

31

173

Back to Instruction

Fair

An experiment with equally likely outcomes.

Tossing a Coin

Rolling a Fair Die

Spinning a Fair Spinner

174

Back to Instruction

Independent Event

When the outcome of one event does not affect the outcome of

another event.

Probability (A and B) =

Prob(A)Prob(B) The prob. of flipping heads

AND rolling 4 on a die.

175

Back to Instruction

Interquartile Range

The difference of the upper quartile and the lower quartile.

25% 25% 25% 25%

Q1 Q2 Q31,3,3,4,5,6,6,7,8,8

Q1 Q2 Q3

1 2 3 4 5 6 7 8

Q1 Q2 Q3

= Q3 Q1 = Q3 Q1= 4

176

Back to Instruction

Lower (1st) Quartile

The median of the lower half of data.

25% 25% 25% 25%

Q1 Q2 Q3

1,3,3,4,5,6,6,7,8,8

Q1 Q2 Q3

1 2 3 4 5 6 7 8

Q1 Q2 Q3

Median

Median

177

Back to Instruction

MeanAverage

The sum of the data values divided by the number of items.

1, 2, 3, 4, 5Set of Data: 1+2+3+4+5

=15

15/5 = 3The mean

is 3.

178

Back to Instruction


The average distance between each data value and the mean.

Find the mean Subtract

the mean from

each data point

Find the mean of the differences2,2,3,4,4

15 5=3

32=1

43=133=0 1+1+0+1+1

=4 5=.8

32=1

43=1

1. 2.3.

179

Back to Instruction

Median

The middle data value when the values are written in numerical order.

1, 2, 3, 4, 5

Median

1, 2, 3, 4 Median is 2.5

1+2+3+4 = 1010/4 = 2.5

180

Back to Instruction

Mode

The data value that occurs the most often.

2, 4, 6, 3, 4

The mode is 4.

2, 4, 6, 2, 4

The mode is 4 and 2.

2, 4, 6, 3, 8

There is no mode.

181

Back to Instruction

Population

A whole group.

Population

Sample

• All m&ms in a bag

• All types of dogs in a dog park

• All students wearing glasses in a classroom

NOT just people in a

place

182

Back to Instruction

What is the probability of flipping a nickel and the nickel landing on

heads?

1 favorable 2 possible

Probability

The ratio of the number of favorable outcomes to the total number of

possible outcomes.

Number of favorable outcomes Total number of

possible outcomes

Probability of an eventP(event)

= 1 or 50% 2

1:2 or 0.5

Many Forms!

183

Back to Instruction

Quartiles

The values that divide the data in four equal parts.

25% 25% 25% 25%

Q1 Q2 Q3

1,3,3,4,5,6,6,7,8,8

Q1 Q2 Q3

1 2 3 4 5 6 7 8

Q1 Q2 Q3

184

Back to Instruction

Random Sample Unbiased Every possible sample of

the same size has an equal chance of being selected

Asking everyone in a classroom if they believe flying is safe.

Asking everyone in a classroom if

they like chocolate.

Asking everyone in a classroom if they like comic

books.

185

Back to Instruction

Range

The difference between the greatest data value and the least data value.

2, 4, 7, 1212 2 = 10The range

is 10.

5, 9, 10, 4040 5 = 35The range

is 35.

1, 5, 9, 1818 1 = 17The range

is 17.

186

Back to Instruction

Sample

A part of a group.

Population

Sample

random or

unbiased

• only red m&ms in a bag

• only poodles in a dog park

• only girls wearing glasses in a classroom

187

Back to Instruction


The ratio of the number of equally likely outcomes in an event to the total number of

possible outcomes.

number of favorable outcomes total number ofpossible outcomes


Find the probability of

getting tails when you flip a coin.

P(tails) = # of favorable outcomes # of possible outcomes

1 2

=

188

Back to Instruction

Upper Quartile

The median of the upper half of data.

25% 25% 25% 25%

Q1 Q2 Q3

1,3,3,4,5,6,6,7,8,8

Q1 Q2 Q3

1 2 3 4 5 6 7 8

Q1 Q2 Q3

Median

Median

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