Township of Union Public Schools s4

TOWNSHIP OF UNION PUBLIC SCHOOLS

MA 412 Functions, Trigonometry and Statistics Curriculum Guide 2013 Curriculum Guide Approved June 2011 Board Members

Francis “Ray” Perkins, President

Versie McNeil, Vice President

Gary Abraham

David Arminio

Linda Gaglione

Richard Galante

Thomas Layden

Vito Nufrio

Judy Salazar TOWNSHIP OF UNION PUBLIC SCHOOLS Administration

District Superintendent …………………………………………………………………...…………………….... Dr. Patrick Martin

Assistant Superintendent …………………………………………………………..……………………….….…Mr. Gregory Tatum

Director of Elementary Curriculum ……………………………….………………………………..…………….Ms. Tiffany Moutis

Director of Secondary Curriculum ……………………………….………………………….…………………… Dr. Noreen Lishak

Director of Student Information/Technology ………………………………..………………………….…………. Ms. Ann M. Hart

Director of Athletics, Health, Physical Education and Nurses………………………………..……………………Ms. Linda Ionta DEPARTMENT SUPERVISORS

Language Arts/Social Studies K-8 ……..………………………………….…………………………………….. Mr. Robert Ghiretti

Mathematics K-5/Science K-5 …………………………………………….………………………………………. Ms. Deborah Ford

Guidance K-12/SAC …..………………………………………………………………………………….……….Ms. Bridget Jackson

Language Arts/Library Services 8-12 ….………………………………….…………………………………….…Ms. Mary Malyska

Math 8-12…………………………………………………………………………………………………………..Mr. Jason Mauriello

Science 6-12……...... …………………………………………………….………………………………….Ms. Maureen Guilfoyle

Social Studies/Business………………………………………………………………………………………..…….Ms. Libby Galante

World Language/ESL/Career Education/G&T/Technology….…………………………………………….….Ms. Yvonne Lorenzo

Art/Music …………………………………………………………………………………………………………..….Mr. Ronald Rago Curriculum Committee

This Advanced Placement Statistics course guide was developed by:

Ines Jaramillo Robert Sukovich Shawn Swingle

The developers would like to Jason Mauriello, Supervisor of Mathematics for his lending his guidance and expertise throughout the development of this curriculum guide. Table of Contents Title Page………………………………………………………………………………………………………………….1 Board Members………………………………………………………………………………………….……………….2 Administration…………………………………………………………………………………………………………….3 Department Supervisors………………………………………………………….…………………………………….4 Curriculum Committee………………………………………………………………….……………………………….5 Table of Contents ………………………………………………………………………….…………………………….6 District Mission/Philosophy Statement…………………………………………….……………………………...…7 District Goals………………………………………………………………………………...……………………..…….8 Course Description………………………………………………………………………………………………...…….9 Recommended Texts……………………………………………………..…………………………………………….10 Course Proficiencies……………………………………………………………………………………………..…….11 Curriculum Units…………………………………………………………………………………………………..…….12 Pacing Guide ………………………………………………………………..……………………………………..…….13 Curriculum………………………………………………………………………………………………………..……….16 Appendix A: Describing Data Project………………..………………………………………………………..……..24 Appendix B: Sample Survey Project ………………………………………………………………………..………25 Appendix C: Baseball Project………………………………………...…………………………………………..……29 Appendix D: New Jersey Scoring Rubric………………………………………………..…………………..………31 Mission Statement

The Township of Union Board of Education believes that every child is entitled to an education designed to meet his or her individual needs in an environment that is conducive to learning. State standards, federal and state mandates, and local goals and objectives, along with community input, must be reviewed and evaluated on a regular basis to ensure that an atmosphere of learning is both encouraged and implemented. Furthermore, any disruption to or interference with a healthy and safe educational environment must be addressed, corrected, or when necessary, removed in order for the district to maintain the appropriate educational setting.

Philosophy Statement

The Township of Union Public School District, as a societal agency, reflects democratic ideals and concepts through its educational practices. It is the belief of the Board of Education that a primary function of the Township of Union Public School System is to formulate a learning climate conducive to the needs of all students in general, providing therein for individual differences. The school operates as a partner with the home and community. Statement of District Goals

 Develop reading, writing, speaking, listening, and mathematical skills.  Develop a pride in work and a feeling of self-worth, self-reliance, and self- discipline.  Acquire and use the skills and habits involved in critical and constructive thinking.  Develop a code of behavior based on moral and ethical principals.  Work with others cooperatively.  Acquire a knowledge and appreciation of the historical record of human achievement and failures and current societal issues.  Acquire a knowledge and understanding of the physical and biological sciences.  Participate effectively and efficiently in economic life and the development of skills to enter a specific field of work.  Appreciate and understand literature, art, music, and other cultural activities.  Develop an understanding of the historical and cultural heritage.  Develop a concern for the proper use and/or preservation of natural resources.  Develop basic skills in sports and other forms of recreation. Course Description

This course follows a structured scope and sequence, introducing, reinforcing and extending topics identified by the Common Core State Standards. This course will prepare students for college level courses in mathematics. The course is divided into three units covering the traditional skills and concepts required for advancement into pre-calculus in a rigorous college preparatory program.

Students will model and solve algebraic problems that involve the study of linear, polynomial, quadratic, radical and logarithmic functions. Students will model and solve basic trigonometry, trigonometric identities, equations and application problems. Students will learn a variety of random sampling methods, describe quantitative and categorical data sets, and calculate the probability of events.

Each of the three units will include the use of group explorations, scientific and graphing calculators, and computer software to study real world problems solving techniques and presentation strategies. Recommended Textbooks

Student Texts:

College Algebra & Trigonometry (5th edition) (Lial, Hornsby & Schneider) - Pearson

Statistics: The Art and Science of Learning from Data (Agresti & Franklin) - Pearson Course Proficiencies

EACH STUDENT WILL BE ABLE TO: Create and interpret graphs from data and calculate descriptive statistics Calculate and interpret correlation between two variables Know the different ways of randomly selecting samples from a population while considering sources of bias Calculate the probabilities of real world phenomena

Find values of trigonometric functions for acute and general angles. Find exact and approximate values for the six trigonometric functions. Verify trigonometric identities, simplify/evaluate expressions and solve trigonometric equations. Identify graphs of the basic trigonometric functions Understand and apply trigonometric functions to solve real-life problems about measurement. Choose the appropriate trigonometric function to find missing parts of right and oblique triangles. Use identities to find values of trigonometric functions and to solve trigonometric equations.

Graph and solve functions and extract information from multiple forms. Solve absolute value equations and inequalities. Solve linear systems by graphing, substitution, elimination, and the use of matrices. Perform operations, inverses, and determinants of matrices. Perform all operations with polynomials, and to factor polynomials. To use the fundamental theorem of algebra to find all zeros of a polynomial. To determine if a function has an inverse and if it has an inverse, find the equation of the inverse. Apply properties of exponents and logarithms. Use algebraic expressions as models of real-life situations. Examine and solve quadratic models involving objects, parabolic shaped regions and quantities related to time Curriculum Units

Unit 1: Trigonometry Concepts and Applications

Unit 2: Statistics: Gathering and Interpreting Categorical and Quantitative Data Gathering and describing Data Interpreting Categorical and Quantitative Data Probability

Unit 3: Functions, Operations and Graphs Functions: Linear, Quadratic, Rational, Exponential and Logarithmic Solving systems of equations and inequalities using matrices Unit 1: Trigonometry Concepts and Applications Title Section Number of Days (45)

Trigonometric Functions 5.1-5.4 10 Circular functions and their graphs 6.1-6.4 10 Trigonometric Identities and 7.1-7.7 20 Equations Applications of Trigonometry 8.1-8.2 5

Unit 2 - Statistics: Collecting and analyzing data, probability Title Section Number of Days (45)

Introduction to Statistics and How to Statistics: 1.1-1.2 4 Learn from Data

Exploring Data with Graphs and Statistics: 2.1-2.5 12 Descriptive Numerical Summaries

Association: Statistics: 3.1-3.3 9 Contingency, Correlation, and Regression

Experiments and Sampling Methods Statistics: 4.1 to 4.4 11 Statistics: 5.2-5.4 9 Probability

Unit 3: Functions, Operations and Graphs

Title Section Number of Days (90)

Review sets, polynomials and radicals Supplementary Materials 6 Equations and Inequalities 1.1-1.8 12 Graphs and Functions 2.3-2.7 12 Polynomial and Rational Functions 3.1-3.5 10 Inverse, Exponential and Logarithmic 4.1-4.6 22 Functions Systems and Matrices 9.1-9.3, 9.5-9.8 23 Review 5 Unit 1: Trigonometry Concepts and Applications

Essential Questions Instructional Objectives/ Skills Activities Assessments and Benchmarks (CPIs) What relationship exists among the sides To find the values of the six Cooperative Class work of a right triangle? trigonometric functions and use learning groups them to solve right triangles G-SRT.6, 8 How can you convert an angle measured To find measure of angles in Discussion Homework in degrees to radian measure? standard position using degree Drill and and radian measure F-TF.1, 2 Practice Why must the angle  be measured in To calculate arc lengths and areas Drill and Class work radians when finding the arc length of a of sectors G-C.5 Practice sector of a circle? Is trigonometry used in real life? Application problems Cooperative Class work and F-TF.1, 2, G-C.5 learning groups Homework What is the reference angle for a non- To evaluate trigonometric Drill and Class work quadrantal angle? functions of any angle Practice F-TF.5 What are you finding when you take the To evaluate inverse trigonometric Discussion Class work and inverse of the sine, cosine, or tangent functions Drill and Homework functions? F-TF.6, 7 Practice What given information indicates using the To use the Law of Sines and the Discussion Class work and law of cosines instead of the law of sines? Law of Cosines to find the sides Homework and angles of a triangle. G-SRT.10,11

What is the definition of the terms cycle To graph sine, cosine, and tangent Cooperative Class work and period of a trigonometric function functions. To give the amplitude, learning groups graph? period, intercepts, maximum, and Use of graphing minimum F-TF.5 calculators What is a trigonometric identity? To use trigonometric identities to Discussion Class work and simplify expressions and to verify Drill and Homework other identities F-TF.8 Practice Can you describe three techniques that To solve trigonometric equations Drill and Class work and you might use to solve a trigonometric F-TF.7 Practice Homework equation? What are some of the uses of the sum and To evaluate trigonometric Discussion Class work and difference formulas? functions of the sum or difference Drill and Homework of two angles F-TF.9 Practice Unit 2a: Interpreting Categorical and Quantitative Data

Essential Questions Instructional Activities Assessments Objectives/ Skills and Benchmarks (CPIs) 1. Identify center, spread, 1. Instructor and student use of interactive computer software Use given data of test 1. How can we construct clusters, outliers and other applet to demonstrate resistance of mean and median by outliers grades from the and interpret unusual features of in a data set. previous statistics graphical displays of univariate data by reading test to answer distributions of graphical representations. 2. Use of correlation by eye computer applet designed to aid questions 1-3 univariate data? S-ID2 students in recognizing strength of correlation. (stemplot, histogram, 58, 89, 67, 99, 74, 91, 3. Use Microsoft Excel computer program to complete least cumulative frequency 2. Calculate center, spread 84, 86, 70, 73, 97, 61, squares regression project (See Appendix C ) plot) and position of univariate 52, 88, 55, 12, 78, 60 data S-ID3 4. Organize univariate data into logical graphical representations 1. Calculate mean, 2. How can we using the graphing calculator that can be used to make conclusions 3. Compare and contrast median, mode, summarizing about univariate distributions. distributions of features of different range, and univariate data? univariate distributions. 5. Enter data into graphing calculator and run one variable standard S-ID3 statistics to find the mean, median, mode, range, standard deviation of data. 3. How can we compare deviation, percentiles, and z-scores for univariate data. distributions of 4. Analyze patterns in 2. Construct a stem univariate data (back- scatterplots, recognize 6. Estimate population percentages using normal distribution. leaf plot of the to-back stem plots and correlation and linearity. Use calculators, spreadsheets, and tables to estimate areas under data. parallel boxplots)? Find least-squares the normal curve regression line and verify its 3. Describe the 4. How can we explore validity by checking residual 7. Check the validity of least-squares regression by analyzing distribution of bivariate data? plots, outliers, and patterns in residual plots the data. influential points. S-ID6 Calculate 5. How can we explore 8. Fit a function to the data, use linear, quadratic and exponential boundaries for categorical data? 5. Construct and interpret functions fitted to data to solve problems in the context of the data. and make representations of mention of any categorical data. S-ID5 9. Construct and interpret frequency tables, bar charts, and other outliers. representations of categorical data. (See Appendix A) Unit 2b: Collecting data and randomization Essential Questions Instructional Objectives/ Activities Assessments Skills and Benchmarks (CPIs) 1. What are the methods of 1. Understand methods of 1. Discussion of different 1. Gathering Data Sample Problems. A data collection? data collection. S-IC3 types of bias including survey is to be conducted in your high 2. Identify characteristics of sampling bias, school. There is to be a total of 40 students 2. How can we conduct a well-designed, well- response bias, in the sample. Describe how you would random sampling using conducted survey. S-IC3 nonresponse bias, choose the participants if: stratified, cluster, 3. Randomly select from a observer bias. i. There are to be the same systematic, and simple population in order to 2. Plan a well-designed number of freshman, random sampling? have a sample from survey. sophomores, juniors, and which valid conclusions 3. Draw an appropriate seniors in the sample. can be drawn.S-IC4 sample from the ii. There are to be the same 3. How can we plan and 4. Identify different population. number of males and females in conduct surveys to avoid sampling methods and 4. Identify possible the sample. bias? sources of bias. S-IC4 sources of bias. iii. There are no restrictions on the 5. Identify characteristics of 5. Analyze sample data choice of the participants. a well designed, well appropriately. iv. Identify the source of the bias 4. When is it appropriate to conducted experiment.S- 6. Complete Sample and specify the direction of the use each of the following IC4 Survey Project (Project bias. experimental techniques description in 2. A flour company wants to know will be discussed: Appendix B) what fraction of Minneapolis randomization, blinding, households bake tier own bread. An double blinding, SRS of 500 residential addresses is replication, and the drawn and interviewers are sent to placebo effect? these addresses. The interviewers are employed during regular 5. How can we generalize working hours on weekdays and results and types of they interview only during those conclusions that can be hours. drawn from observational studies, experiments, and surveys? Unit 2c: Calculating Probability Essential Questions Instructional Objectives/ Skills Activities Assessments and Benchmarks (CPIs) 1. How can we use the Law of 1. Interpret probability including long- 1. Calculate probability based 1. A set of 2000 measurements Large Numbers to run relative frequency on both independent and has a symmetric, mound- understand probability? interpretation. S-CP2 dependent events shaped distribution. The 2. How can we use the 2. Find probabilities based on mean Is 5.3 and the standard Addition rule, distributions of discrete random 2. Find probability based on deviation is 0.7. Determine multiplication rule, variables. S-MD2 binomial and geometric an interval that contains conditional probability, and 3. Simulate the random behavior of random variables. Use approximately 1360 data independence to find the events based on probability graphing calculator functions values. probability of an event distributions. S-MD1 binompdf and binomcdf to 2. In a group of 100 scouts who occurring? 4. Calculate expected value and calculate binomial took the physical exam for 3. How can we combine standard deviation of a random probabilities. summer camp, 20% had independent random variable and linear transformations type A blood. Six percent variables of a random variable. S-ID6 3. Find the mean and standard had both blond hair and type 4. How can we use the normal 5. Differentiate between independent deviation for sums and A blood. Find the probability distribution to understand and dependent events.S-CP2 differences of independent that one scout selected at probability? 6. Identify properties of a normal random variables. random will have blond hair, distribution and use normal given that the blood test distribution tables S-MD3 4. Find probabilities based on reveals type A. normally distributed random 3. Rogers High will play variables. Memorial High in baseball six times during the 5. Use sampling distributions upcoming season. Assume reach conclusions about the teams are of equal sample data. ability; that is, p = .5. Within the context of a binomial experiment, what is the probability that: Rogers will win 4 games and lose 2 Rogers will win at least 4 games? Unit 3 – Functions, Operations, and Graphs Essential Questions Instructional Objectives/ Activities Assessments Skills and Benchmarks (CPIs) How do we solve a quadratic To solve and graph a linear Drill/Practice Classwork/homework equation? equation. A-REI.4ab

What is a complex number? To use properties of Drill/practice Classwork/homework complex and imaginary numbers. N-CN 1,2

Can we use graphs of To use graphs of quadratic Cooperative Groups Classwork/Homework quadratic and linear and linear equations/systems in real equations/systems to solve life? real world problems.A- REI2,3

How do we solve an To solve and graph an Drill and practice Classwork/Homework inequality/systems of inequality/system of inequalities? inequalities. A-REI3

Are there any other types of To define, solve, and graph Drill and practice Classwork/Homework equations? a rational equation. A.REI-2

How do I recognize a To define a function and the Discussion Classwork/Homework function? elements of a function. F-IF1-3

What kinds of functions To identify the types of Cooperative Groups Classwork/Homework exist? functions.F-IF1-3

How do I construct a graph To graph a function by of a function without any creating a chart. F-IF7 Drill/practice Classwork/Homework electronic aid?

What is a zero of a function? To determine whether x-k is Discussion/drill and practice Classwork/Homework a factor of f(x). A-APR3

What is a parabola? To define and graph a Drill and practice Classwork/Homework parabola. A-REI 4a,b

Can we graph functions To graph and model higher Drill and practice Classwork/Homework higher than degree two? order functions. A.APR3

What is an asymptote? To define asymptote and identify the asymptotes of a Discussion Classwork/Homework function. F-EE1b,c

What is an inverse function? To solve and graph inverse Drill and practice Classwork/Homework functions. F-BF4

What is an exponential To define and graph an Discussion/drill and practice Classwork/Homework function? exponential function. F-LE3, F-IF7e

Can we graph logarithmic To define and graph a Cooperative groups Classwork/Homework functions? logarithmic function. F-LE4

Can we apply an To apply the properties of an exponential function to a real exponential function to a real Drill and practice Classwork/Homework world situation? life situation. F-LE1b,c

How do we solve a system To solve systems of of equations? equations by graphing, elimination, and substitution. Discussion/drill and practice Classwork/Homework A-REI5,6

Is there another way to solve To solve a system of Drill and practice Classwork/Homework a system of equations/What equations using an is a matrix? augmented matrix. A- REI5,6N-VM6

What is the determinant of a To define and calculate the Discussion/drill and practice Classwork/Homework matrix? determinant of a matrix.N- VM 6

Do matrices have any other To apply operators to Drill and practice Classwork/Homework properties? matrices.N-VM7,9

Can I apply matrices to real To use matrix multiplication Cooperative groups Classwork/Homework world situations? to model house plans.N- VM6

What is a nonlinear system To solve a nonlinear system Drill and practice Classwork/Homework of equations? of equations. A-REI 6 Classwork/Homework When using linear To solve systems of Drill and combinations, why would equations in 3 and 4 practice/cooperative groups you want the coefficient of variables algebraically. A- one of the variables to be REI6 opposite? Appendix A: Statistics Quantitative Data Project Due: ______

Objective To use descriptive statistics to organize, summarize, and graphically represent data.

Project Requirements 1. Collect quantitative data on a variable of interest to you. List the values of the observations. (n ≥ 30) Sample topics are listed on the back of this page. 2. Determine if the variable is discrete/continuous. Explain why. 3. Make a frequency table from the data. 4. a. Construct a dotplot from the data. Describe the main features of the dotplot. b. Construct a stem and leaf plot from the data. Describe the main features of the stem and leaf plot. c. Construct a histogram from the data. Describe the main features of the histogram. 5. Determine the shape of the distribution of the data. 6. Calculate the mean, median and mode of the data. 7. Determine whether the mean or median is a better estimate of the center for your data? Explain why. 8. Calculate the range, variance and standard deviation of the data. 9. Does the empirical rule apply to your data? Explain why or why not? 10. Calculate the 5-Number Summary for the data. 11. State and interpret the quartiles for the data. 12. Calculate the interquartile range for the data. 13. Are there any outliers in your data? Show your calculations. 14. Construct a boxplot for the data. 15. Calculate the z-score for the last observation you collected based on your data. Show your calculation. Interpret this z-score. 16. Give a brief 2-minute presentation showing the results of your descriptive statistic analysis.

Complete all starred requirements using a computer (preferably Excel). Appendix B: Statistics Sample Survey Group Project Due:

Objective: Design and implement an observational study to answer your topic question.

Requirements Each student must hand in their own individual project. Topic questions must be approved by the teacher. Steps 2-7 should be the same for every member in your group. Steps 8-12 should be different for every member.

On your title page, write your name and topic question. Also list your group members. Please number the requirements in your final report.

Group Project Requirements 1. Each person in your group must decide on an individual topic question with a common group theme. 2. Combine all the topic questions from your group into one survey. Think carefully about the wording of these questions. Include this survey in your individual report. 3. What is the population for your study? 4. What sampling method will your group use to gather your data? What will the sample size be? Explain why your group chose that sampling method over the others. 5. Explain exactly how the subjects for your sample will be chosen. Will the sample be representative of the population? Be as specific as possible. 6. Collect the sample based on the survey your group prepared and sampling method your group selected. (This step does not need to be included in the final written report.) 7. Discuss any problems that your group ran into with the sampling process. Are there any biases that may occur as a result of the sample your group collected? Explain. (It’s OK to mention problems or biases that you find. In practice, almost no sample is without its share of problems. Just mention the issues your group ran into and how your group dealt with them.) The group aspect of the project is complete. The rest of the project will be individual, using the data for your individual topic question only.

Individual Project Requirements 8. Display the data collected on your individual topic question from the survey. 9. Construct a table to display the data. 10. Make an appropriate graph based on your data. 11. If the data is categorical, calculate the relative frequency of each category. If the data is quantitative, calculate the mean, median, mode, standard deviation. 12. Summarize the conclusions that you found based on the graphs and calculations. Explain the results of the sample.

Results Presentation Students must present their findings to the class in a clear and concise manner with emphasis on the use of proper statistical vocabulary and terminology.

Sampling Project Holistic Scoring Rubric 1 2 3 4 5 6 Topic Mostly incorrect Mostly correct Mostly correct Mostly correct Correct grammar & Correct grammar Question grammar & grammar & grammar & grammar & punctuation; & punctuation; punctuation; punctuation; punctuation; punctuation; Unbiased wording Unbiased wording Biased wording Biased wording Unbiased wording Unbiased wording

Population Description of Description of Description of Somewhat detailed Detailed Detailed incorrect population incorrect correct description of description of description of is given population is given population is correct population correct population correct population given is given is given is given

Sampling Just mention which Incorrect reasons Somewhat correct Somewhat correct Clearly stated Clearly stated Method sampling method you for choosing your reasons for reasons for reasons for reasons for choosing chose sampling method choosing your choosing your choosing your your sampling sampling method sampling method sampling method method

Description Missed many steps in Mentioned most Detailed description Detailed description Detailed Detailed Of Sample the data collection steps in the data of some steps in the of most steps in the description of most description of process collection process data collection data collection steps in the data every step in the process process collection process data collection process

Problems Did not discuss any Discussion of Discussion of Discussion of Discussion of Discussion of sampling problems sampling sampling sampling sampling problems sampling problems without problems without problems without with possible problems with possible solutions possible solutions realistic solutions solutions realistic solutions Table of Inaccurate and Inaccurate table Accurate table or Accurate table and Somewhat neat Neat and accurate Data sloppy table and and graph that graph that graph that displays and accurate table table and graph graph that displays displays your data displays your data your data and graph that that displays your your data displays your data data

Descriptive No calculations of Inaccurate Accurate Accurate Accurate Accurate Statistics descriptive statistics calculations of calculations of calculations of calculations of calculations of descriptive descriptive descriptive statistics descriptive descriptive statistics statistics statistics statistics

Conclusions Conclusion is not well Conclusion is not Somewhat clearly Somewhat clearly Somewhat clearly Clearly stated and stated and not well stated, but is stated and well- stated and well- stated and well- well-thought out supported by the somewhat thought out thought out thought out conclusion is data supported by the conclusion is conclusion is stated conclusion is stated stated and data stated and not and somewhat and supported by supported by the supported by the supported by the the data data data data Appendix C: Statistics Baseball Project (Linear Regression) Objective: To describe the association between quantitative variables and to predict values of the response variable based on the values of the explanatory variable. In baseball terms, we will find which variable is most correlated with winning and predict the number of wins based on this variable. All starred steps must be done on the computer using EXCEL.

Requirements 1. Collect the following baseball data from the ______baseball season: Hitting Stats: R, HR, SB, BA, ______Pitching Stats: Wins, R, SO, ______Select one more Batting and one More Pitching statistic that you want to explore Directions a. Go to http://www.baseball-reference.com/leagues/MLB/ b. click on the link for that year which brings you to Team and League Standard Batting c. Copy and paste batting and pitching statistics into EXCEL. (be sure to select everything from “Team and League Standard Batting” down to the bottom of the page. d. Put Batting on Sheet 1 and rename Batting, Put Pitching on Sheet 2 and rename Pitching e. Highlight then Copy/Paste pitching wins column into batting Stats page. f. Clean up the data and delete all unnecessary columns. (be careful) g. Print out batting data landscape on one page h. Print out pitching data landscape on a separate page.

2. Use EXCEL to construct 8 scatterplots that plots each quantitative variable as the x variable against Wins as the y variable. (Note: since every win is credited to a pitcher on the team, pitcher wins is the same as team wins. Rename Sheet 3 Scatterplots and put all scatterplots there. INSERT>CHART>SCATTERPLOT>SELECT COLUMNS>LABEL AXES>ADD AS OBJECT Add the regression equation (trend line) and r2 value by right clicking on a point on the scatterplot and clicking “add trendline”; then on the options tab add the equation and r2 value. Print scatterplots all on the same page (create as objects in one sheet instead of giving each scatterplot its own sheet.) On a separate page, discuss any associations visible in each scatterplot.

2. Calculate and interpret the correlation for each of these eight variables with Wins. Comment on the validity of the correlation. 3. Interpret r2 for each of the eight variables with Wins.

4. Are there any influential points in any of your scatterplots? If so, identify them by Team name.

5. Based on the results of steps #2-4, identify which of the eight variables seems to be the best predictor of Wins? Why?

6. Use the regression line of the variable you selected in step #5 to predict the number of Wins the New York Yankees should have had, based on this variable.

7. Calculate and interpret the residual for the New York Yankees based on the same regression line.

8. Use EXCEL to construct a residual plot for the same regression you chose in step #5. Does this residual plot verify that the least squares regression line fits the data well? Explain. (Show the predicted values, residuals and residual plot all on the same page.) Display the data collected on your individual topic question from the survey. 9. Construct a table to display the data. 10. Make an appropriate graph based on your data. 11. If the data is categorical, calculate the relative frequency of each category. If the data is quantitative, calculate the mean, median, mode, standard deviation. 12. Summarize the conclusions that you found based on the graphs and calculations. Explain the results of the sample. Results Presentation Students must present their findings to the class in a clear and concise manner with emphasis on the use of proper statistical vocabulary and terminology. Appendix D: New Jersey Scoring Rubric