blair mod 3 stats teacher resources

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OUTLINE OF RESOURCES

Getting StartedActivities and Demonstrations

Building Vocabulary: Crossword Puzzle 92

Digital Connection

Videocassette Series:Statistics: Decisions Through Data 93

DVD/Online Series:Against All Odds: Inside Statistics 93

Frequency DistributionsActivities and Demonstrations

Application Activity: Organizing and Interpreting Data 93

Application Activity:Describing Data 94

Measures of Central Tendency

Digital Connection

Technology Application Activity:PsychSim: Descriptive Statistics 94

Measures of Variation

Digital Connection

DVD: Handling Variability 94

Normal DistributionDigital Connection

DVD:Describing Data 95

Activities and Demonstrations

Cooperative Learning Activity:A Tasty Sample(r): Teaching About Sampling Using

M&Ms 95

Comparative StatisticsActivities and Demonstrations

Application Activity: The Water Cup Toss Test 96

Correlation CoefficientActivities and Demonstrations

Application Activity: Creating a Scatterplot 96Application Activity: Correlation and the ChallengerDisaster 97

Module 3 Psychologys Statistics 91

M O D U L E

Psychologys Statistics

3

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Statistical InferenceActivities and Demonstrations

Application Activity: When Is a Difference Significant? 97

Handouts31 Crossword Puzzle

32 Presidents Ages at Time of Inauguration33 Student Survey

34 M&M Data Sheet

35 The Water Cup Toss Test

36 Charting Correlations on Scatterplots

Blackline Masters31a ChallengerCorrelations

31b ChallengerCorrelations

32 Figure 3.1

33 Figure 3.2

34 Figure 3.3

35 Figure 3.4

36 Figure 3.6

37 Figure 3.738 Figure 3.9

39 Figure 3.10

310 Figure 3.11

MODULE ESSENTIAL QUESTIONS AND OBJECTIVES

After completing their study of this module, students should be able to:

analyze characteristics of a distribution of scores (including frequency distribution,measures of central tendency, and measures of variation).

interpret data represented on a normal distribution.

describe the difference between percentage and percentile rank.

define correlation coefficient and interpret positive and negative correlations.

explain what it means when a research result is statistically significant.

MODULE OUTLINE

Getting Started


Building Vocabulary: Crossword Puzzle

Concept: Students can reinforce the definitions of the terms in this module by com-

pleting this crossword puzzle that incorporates a matching activity.

Materials: Handout 31

Description: Distribute the handout to students. Allow them to complete the puzzle

as a study tool for assessments that might be used in coordination with this module.

92 Module 3 Psychologys Statistics



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Discussion: By coupling a matching activity with a crossword puzzle, students get two

different ways to process the information from this module.

Digital Connection

Videocassette Series: Statistics: Decisions Through Data

This series consists of five one-hour videotapes and a 260-page Users Guide, which pro-

vides program summaries and classroom exercises. An important strength of the series,

which makes it particularly useful at an introductory level, is its use of everyday examples

to illustrate basic statistical concepts. For example, the first program covers descriptive sta-

tistics through the introduction of a number of data sets, including physical measurements

of army soldiers, pollution in Chesapeake Bay, Hispanic FBI agent discrimination, and the

reliability of space shuttle rocket boosters. It presents data gathering and accompanying

statistical analysis as important tools in helping us to see what the unaided eye would miss.

It shows, for example, how bar graphs and the use of medians to compare weekly wages of

Colorado Springs municipal clerical and maintenance workers were used in identifying

and eventually correcting wage discrepancies. This approach to statistics runs throughout

the series. Additional programs cover the normal curve, regression, scatterplots, correla-

tion, design of experiments, sampling distributions, hypothesis testing, and confidence

intervals. (Consortium for Mathematics and Its Applications [COMAP], 60 minutes each)

For ordering information, please visit www.comap.com.

DVD/Online Series:Against All Odds: Inside StatisticsFrom the Annenberg/CPB collection, this series consists of 26 half-hour programs that

cover every aspect of statistics. You might consider purchasing the programs for your

department for selected use in introductory psychology and in more advanced courses,

particularly those in statistics and methodology. Hosted by Teresa Amabile of Brandeis

University, the programs intersperse lectures on key concepts with mini-documentaries

from everyday life. For example, in one sequence viewers see how women armed with

statistical information were able to win a hiring discrimination suit. Another documen-

tary demonstrates the principles of behavioral correlation with the examination of twins

who were reared apart. Specific program titles from which you may want to select small-

er segments for showing in connection with text material include What Is Statistics?

Picturing Distributions, Describing Distributions, Normal Distributions,

Correlation, The Question of Causation, Samples and Surveys, Confidence

Intervals, and Significance Tests. (Annenberg/CPB, 30 minutes each) For ordering

and viewing information, please visit www.learner.org/resources/series65.html.

Frequency Distributions


Application Activity: Organizing and Interpreting Data

Concept: This activity, suggested by David Moore, involves the ages of American pres-

idents at the time of their inauguration. It gives students some elementary practice in

organizing and interpreting real data.


Description: Students can organize the data into a bar graph, determine mean, medi-

an, and mode, and even calculate the range and standard deviation.

Discussion: For your information, the distribution of ages is roughly symmetric. The

mean age of a new president is 54.83, the mode is 51, and the median is 55. The range

is from 42 to 69, or 27 years, and the standard deviation is 6.27.

Source: Moore, D. S. (1995). The basic practice of statistics. New York: Freeman.




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Application Activity: Describing Data

Concept: Descriptive statistics is effectively taught by example. In fact, it may be best

to illustrate the basic concepts through data provided by the students themselves.


Description: Handout 33 allows you to collect a variety of data. You can add and

delete questions as you like. Reminding students to bring along hand calculators will

facilitate the entire process. Depending on class size and time constraints, you can usethe class period to organize and describe the data, or you can collect the surveys and pre-

pare a data sheet. In the following class period, students can, either individually or in

small groups, calculate the final statistics.

Discussion: Concepts including distributions, percentile rank, central tendencies, vari-

ation, and correlation can be illustrated with these data. You can also use the data to test

for differences between groups. For example, do first-borns have a higher GPA or high-

er SAT scores? Similarly, do males and females differ in GPA and SAT scores?

Measures of Central Tendency

Digital Connection

Technology Application Activity: PsychSim: Descriptive Statistics

Concept: PsychSim is a computer program published by Worth that provides hands-onexperience with different concepts in psychology.

Materials: PsychSim program; computer access, preferably in a lab setting for use with

an entire class.

Description: This program begins by explaining data distributions, showing how they

are more clearly depicted on bar graphs. It allows students to practice calculating meas-

ures of central tendencymean, median, and modeand measures of variation.

Students see how the measures describe data differently.

Discussion: The program can be used effectively to review all the material on descrip-

tive statistics.

Reteaching Option: PsychSim can be used as a reteaching tool for students who do

not understand the concepts when they are first taught. Installing the program onto a

classroom computer and assigning students to use it during a study hall period or dur-

ing an independent learning time would be a valuable use of this program.

Measures of Variation

Digital Connection

DVD: Handling Variability

This video uses the measurement of blood pressure to illustrate how multiple measures

may produce widely different results. Both measurement errors and actual

fluctuations in the parameters being measured create variability. The distinction

between systematic and random error is used to introduce statistical techniques that

take these sources of error into consideration and permit us to make valid inferences and

decisions about the data. (Films for the Humanities and Sciences, 25 minutes) For order-

ing information, please visit www.films.com.




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Normal Distribution

Digital Connection

DVD: Describing Data

This program begins with the distinction between qualitative and quantitative data and

then describes various ways of representing data, including histograms, bar charts, and

dot plots. The program also explains the various measures of central tendency and how tocalculate mode, median, and mean. The advantages and disadvantages of each measure are

reviewed. The video describes variation in data and how it is measured and described,

focusing on the standard deviation and the bell-shaped distribution that statisticians refer

to as the normal curve. (Films for the Humanities and Sciences, 25 minutes) For order-

ing information, please visit www.films.com.


Cooperative Learning Activity:A Tasty Sample(r): Teaching About Sampling

Using M&Ms

Concept: Randolph Smith proposes this activity that helps students see how represen-

tative samples are chosen and aid in generalization. Knowledge of how to take a repre-

sentative sample is important to understanding the research process.

Materials: A small package of M&Ms for each student (NOTE: Students with food aller-gies may want to abstain from this activity); a calculator (handy, but not required);

Handout 34

Description: Allow each student to choose an intact random sample (one pack of

M&Ms) from the population of samples. Students should examine their data and enter it

on the Handout 34 data sheet. Have them convert their raw data into percentages.

Students should then generate a hypothesis about the distribution of M&M colors in the

population based on the students sample. Students should then form pairs to pool their

data to generate a joint hypothesis. Finally, pool the data from the entire class to gener-

ate an overall hypothesis.

Discussion: Many interesting research questions can be addressed with this activity.

First, since sample sizes are so small with fun-size packs, the accuracy of percentages will

be low. They will see that as they combined their data, the accuracy of the percentages

increased. Discuss how larger sample sizes yield greater accuracy. You may even want to

have larger bags of M&Ms handy to test this assertion. Another issue concerns qualitycontrol. Large manufacturers such as M&M/Mars strive for quality control, but may not

be able to achieve it with each bag of candy. Randolph Smith has collected data with these

M&M samples in his classes and on two out of three occasions, he found a significant

departure from the expected data (p < .001 in each case) you could discuss how compa-

nies can test for quality control by using random sampling techniques.

Interestingly enough, M&M/Mars, Inc., seems to be quite concerned that the per-

centages of colors in each bag of candy are consistent. On their website,

us.mms.com/us/about/products, the company lists a breakdown of the percentages

of each color in each type of bag of candy they distribute. Students can check out the

percentages of the particular type of M&Ms they are using in class to determine if their

sample is representative.

Source: Smith, R. A. (1999). A tasty sample(r): Teaching about sampling using M&Ms. In L. T.Benjamin, B. F. Nodine, R. M. Ernst, & C. T. Blair-Broeker (Eds.), Activities handbook for the teaching

of psychology (Vol. 4). Washington, DC: American Psychological Association.




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Comparative Statistics


Application Activity: The Water Cup Toss Test

Concept: Vic Mankin proposes an active way to compute percentile rank using a sim-

ple tossing activity.

Materials: 9-ounce cups (one per group of students); 15 paper clips per student tossing;

Handout 35

Description: Divide students into groups of 4. Have one student stand 4 feet away from

a free-standing 9-ounce paper cup. There should not be a backboard for the cup. A stu-

dent not tossing the clips can hold the cup to keep it stable. Students should toss a stan-

dard paper clip into the cup. Leaning and stretching are permitted so long as feet remain

4 feet from cup. Each student should take fifteen throws. The score is the number of

paper clips in the cup for each student.

After all students have completed the tossing activity, students should compile their

data on Handout 35. Students should record with a tally mark how many paper clips

remained in the cup for their particular turn in the Tabulations column. In the

Frequency column, students should calculate the number of tally marks in the

Tabulations column and record the number. Then, students should begin with the row

labeled 15 and record the number of the row in the Cumulative Frequency column.In the next row, labeled 14, the students should take the number in the Frequency

column and add it to the number from row 15 to get the cumulative frequency for row

14. Students should repeat this process for each row. If a row does not have any tally

marks, then the cumulative frequency will remain the same as the previous row.

Students can now calculate the percentile rank for each row by taking the rows cumu-

lative frequency and dividing that number by the total number of observations (in this

case, the total number of tally marks) and then multiplying that result by 100.

At this point, students should then compile their data into a class-wide percentile

chart. Repeat the same process, only now with the whole-class data. Students can see

how their own data compares to the class data.

Discussion: Students often find percentile rank confusing, even though they have been

measured according to percentile rank throughout their lives. Standardized tests reveal

percentile rank of students scores as they are compared to the population of students

who took the test. This exercise helps students see where their own skill at paper toss-ing falls into a comparison of other students who engaged in the same test.

Source: Mankin, V. (1973). Teaching tips: The water cup toss test. Professional Psychology, 4(1),107108.

Correlation Coefficient


Application Activity: Creating a Scatterplot

Concept: Scatterplots are simple, visual tools that show the degree of correlations. This

worksheet provides some simple data that can be plotted on the graph to show a posi-

tive correlation between TV watching and grade point average (GPA).


Description: Pass out the handout, instructing students to plot the data sets for thehours of TV watching and grade point average (GPA) on the graph. They should note

what kind of correlation the graph shows: positive, negative, or zero correlation (posi-

tive is the correct answer).




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Discussion: Correlations become more concrete when taught visually. This activity

enables students to create their own scatterplots of correlational data.

Application Activity: Correlation and the Challenger Disaster

Concept: Illusory correlationsfor example, the false belief that infertile couples are

more likely to conceive a child after adopting a babymay result from a failure to look

at all the relevant data. Rob McEntarffer provides a classroom exercise that demonstrates

how we may also fail to recognize a true correlation because we ignore relevant data.More generally, his exercise introduces students to scatterplots and the meaning of pos-

itive and negative correlations. It also illustrates how correlational research can be

important to everyday decision making.

Materials: Blackline Masters 31a and 31b

Description: Begin by asking students if they remember from their study of

history what caused the Challengerdisaster. The explosion was attributed to O-ring fail-

ure in low temperatures at the time of launch. Place Blackline Master 31a on the

overhead projector and have students create their own scatterplot. Have them draw a line

of best fit and ask if they see a positive, negative, or no correlation. They should see and

report, No correlation. By looking at this data and considering other factors, NASA

decided to launch. Explain that although NASA did test the O-rings to determine if

there was a correlation between their failure and temperature, they did not take their

tests far enough. The problem was that they did not look at all the relevant data. Theydid not consider the temperatures at which there was not a failure. Place Blackline

Master 31b on the overhead projector. Again have students create a scatterplot and

draw the line of best fit. Ask, Is there a positive, negative, or no correlation? They

should clearly see that there is indeed a negative correlation. Failure of the O-rings tend-

ed to occur at lower temperatures.

Discussion: This vivid example of the reliance on correlation to make important deci-

sions helps show students the value of critical thinking about data. Guiding students

through this activity allows them to see the thought processes people should employ

when evaluating data for decision-making purposes.

Source: McEntarffer, R. (1999). Correlation and the Challengerdisaster. In L. T. Benjamin, B. Nodine,C. T. Blair-Broeker, & R. M. Ernst (Eds.), Activities handbook for the teaching of psychology (Vol. 4).Washington, DC: American Psychological Association.

Statistical Inference


Application Activity: When Is a Difference Significant?

Concept: Differences between the average scores of two groups may be due to chance

variation rather than to any real difference. Only when sample averages are reliable and

the difference between them is large do we obtain statistical significance. You can effec-

tively illustrate the problem psychologists face in judging differences to be significant

with a brief classroom exercise (or you can assign it as an out-of-class project and have

students report their results at the next class session).

Materials: pennies; a flat table

Description: Begin by placing eight to ten pennies on the edge of a smooth table or

desk (requires a steady hand, a little practice, and newer pennies). Jar the table by drop-

ping a book on it so that the pennies will fall. (Do not jar it so hard that they flip.)Count the number of heads, which is likely to be greater than the number of tails. Ask

students to explain for the difference. Most will attribute it to chance. They will note

that, just as when you flip a coin several times, the number of heads and tails may not

be equal.




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Have your students pair off, then distribute eight or ten coins to each pair and

ask them to place the pennies on edge. Walk around the room jarring each table or

desk and have the students report the results to the full class. Write the results on

the chalkboard, carefully keeping track of the total number of heads and tails. As each

student pair reports their results, continue asking the class whether they believe

the difference in the number of heads versus tails is due to chance or to some real

difference.

Discussion: The exercise uses the counterintuitive fact that, due to their construction,

pennies placed on edge on a hard table show a definite tendency to land heads more

often than tails. (In fact, about 4 out of 5 times they will fall heads.) The question

of significance is essentially what psychologists ask when judging the differences

between any two groups. Averages based on more cases, of course, will be more reli-

able. Although there is certain to be considerable variation in the small sample tested

by each student pair, the overall pattern of significantly more heads than tails will

emerge and at some point the majority of students will agree that the difference is not

due to chance. Note that for psychologists, proof beyond a reasonable doubt means that

they do not make much of a difference unless the odds of it occurring by chance are

less than 5 percent.

Source: Lock, R., & Moore, T. (1991). Low-tech ideas for teaching statistics. In F. Gordon & S. Gordon(Eds.),Statistics for the twenty-first century (pp. 99108). Washington, DC: Mathematical Association of

America.




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HANDOUT 31

Crossword Puzzle

Complete the puzzle using terms from this module.

Across

3. A distribution that is symmetrically

shaped

7. The score in a distribution that

appears most frequently

8. Statistics that allow decisions or

conclusions to be made about data

10. The measure of how much scores

may vary around the mean in a

distribution

11. The average of the data, obtained

by dividing the sum by the number

of data points

12. A type of distribution in which a list

of scores is ordered from highest to

lowest

Down

1. ____________ coefficient; a

measure of the strength and

direction of the relationship

between the two variables

2. A comparison of a score to other

scores in an imaginary group of

100 people

4. A statistical measure of the likelihood that the results of a study are due to chance5. The middle score in a distribution when data is in chronological order

6. The difference between the highest and lowest data points in a distribution

9. A comparison of a score to a perfect score of 100

10. Distorted; refers to a graph of data that is not equally distributed around the mean

Name _______________________________________ Period _________________ Date ____________

HANDOUT 31 Module 3 Psychologys Statistics 99

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HANDOUT 32

Presidents Ages at the Time of Inauguration

President Age President Age President Age

Washington 57 Lincoln 52 Hoover 54

J. Adams 61 A. Johnson 56 F. D. Roosevelt 51

Jefferson 57 Grant 46 Truman 60

Madison 57 Hayes 54 Eisenhower 61

Monroe 58 Garfield 49 Kennedy 43

J. Q. Adams 57 Arthur 51 L. Johnson 55

Jackson 61 Cleveland 47 Nixon 56

Van Buren 54 B. Harrison 55 Ford 61

W. H. Harrison 68 Cleveland 55 Carter 52

Tyler 51 McKinley 54 Reagan 69

Polk 49 T. Roosevelt 42 G. H. W. Bush 64

Taylor 64 Taft 51 Clinton 46

Fillmore 50 Wilson 56 G. W. Bush 54

Pierce 48 Harding 55 Obama 47

Buchanan 65 Coolidge 51

1. Display the above data in a bar graph, placing age at inauguration on the vertical axis and the total

number of presidents at each age on the horizontal axis. (Hint: Use bars with intervals of five years each,

beginning with 4045 years and ending with 6570. Use numbers from 0 to 16 on the vertical axis.)

2. Calculate the mean, median, and mode for the presidents ages.

3. Calculate the variance and standard deviation of the presidents ages.

Name _______________________________________ Period _________________ Date ____________

100 HANDOUT 32 Module 3 Psychologys Statistics



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HANDOUT 33

Student Survey

Please provide the information requested. Your personal responses will remain anonymous, so please answer

all questions accurately and honestly.

1. Your age:

2. Your sex (circle one): MALE FEMALE

3. Your high school GPA:

4. Your SAT/ACT score:

5. Your height (in inches):

6. Your weight (in pounds):

7. Your birth order (indicate 1 if only child):

8. Total number of siblings:

9. Your shoe size:

10. Average number of hours you study per week:

11. Average number of hours you sleep per night:

12. Average number of hours you watch TV per week:

13. Average number of hours you exercise per week:

Name _______________________________________ Period _________________ Date ____________




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HANDOUT 34

M&M Data Sheet

Record the number and percentage of each color in your bag of M&M candy.

Name _______________________________________ Period _________________ Date ____________

Color Number of M&Ms Percentage of Color

Brown

Yellow

Red

Blue

Green

Orange




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HANDOUT 35

The Water Cup Toss Test

Percentile Worksheet for Class

Score Tabulations Frequency Cumulative PercentileFrequency

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

Total Number

Percentile Cumulative Frequency 100

Number of observations

Name _______________________________________ Period _________________ Date ____________




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HANDOUT 36

Charting Correlations on Scatterplots

Chart the following data pairs on the graph below. Indicate whether the data resemble a positive correlation,

negative correlation, or zero correlation.

GPA Hours Watching TV per week

3.9 10

3.2 15

2.1 44

1.5 39

1.8 35

2.5 22

2.5 8

3.5 10

4.0 6

3.8 7

3.5 9

2.9 18

2.5 30

3.0 20

3.5 12

2.4 33

2.1 25

4.0 30

Name _______________________________________ Period _________________ Date ____________




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ANSWERS TO HANDOUT 31

Crossword Puzzle

Answers to Handouts Module 3 Psychologys Statistics 105

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ChallengerCorrelations

Make a scatterplot of the following data:

Would you have launched the space shuttle Challenger in cold weather based on

this data?

Temperature Number of O-Ring Failures

53 2

57 1

58 1

63 1

70 2

75 2

BLACKLINE MASTER 31a

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ChallengerCorrelations

Make a scatterplot of these data:

Now, would you have launched the space shuttle in cold weather using this data?

Temperature Number of O-Ring Failures

53 2

57 1

58 1

63 1

66 0

67 0

68 0

69 0

70 0

70 2

72 0

73 0

75 075 2

76 0

79 0

81 0

BLACKLINE MASTER 31b

BLACKLINE MASTER 31b Module 3 Psychologys Statistics 107

COPYRIGHT2

013BYWORTHPUBLISHERS



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Figure 3.1, Page 43

BLACKLINE MASTER 32

108 BLACKLINE MASTER 32 Module 3 Psychologys Statistics

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Figure 3.2, Page 43

BLACKLINE MASTER 33 Module 3 Psychologys Statistics 109

BLACKLINE MASTER 33

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Figure 3.3, Page 44

BLACKLINE MASTER 34

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110 BLACKLINE MASTER 34 Module 3 Psychologys Statistics COPYRIGHT2013BYWORTHPUBLISHERS



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Figure 3.4, Page 45

BLACKLINE MASTER 35

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Figure 3.6, Page 47

BLACKLINE MASTER 36

Cs-Only Club

Number of

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A B C D F

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Central tendency = C Variation: None

Number ofstudents

Everybodys Welcome Club

A B C D F

Grades

Central tendency = C Variation: High

112 BLACKLINE MASTER 36 Module 3 Psychologys Statistics COPYRIGHT2013BYWORTHPUBLISHERS



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Figure 3.7, Page 48

BLACKLINE MASTER 37

36yards

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41yards

45yards

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=40yards

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Figure 3.9, Page 50

BLACKLINE MASTER 38


AssumeJackgets160pointson

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Figure 3.10, Page 51

BLACKLINE MASTER 39

Perfect negative correlation (1.00)

(a)

Perfect positive correlation (+1.00)

(b)

No relationship (0.00)

(c)

COPYRIGHT2




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Figure 3.11, Page 52

BLACKLINE MASTER 310


95

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50

45

40

35

30

25

85

55

60

65

70

75

80

Temperamentscores

Emotionally

reactive

Calm

Heightininches



blair mod 3 stats teacher resources

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