# Syllabus For AP Statistics

## Introduction

We believe that AP Statistics should be an activity centered course in which students routinely use technology to construct their own understanding of the principles and practices of statistics. Therefore, the following syllabus relies heavily on student's active engagement in doing statistics with appropriate technological tools throughout the course. This engagement is achieved by the use of Workshop Statistics: Discovery with Data, (1995) by Allan J. Rossman as the primary text book for the course. Additional support is provided by the use of The Basic Practice of Statistics, (1995) by David S. Moore. Sequencing of the topics in this syllabus differs from the listing of topics in the AP Statistics Course Description; however, this syllabus will treat all of the topics in the published AP Statistics curriculum.

## Course Outline

 Resources Key:  Rossman = Workshop Statistics: Discovery with Data by Allen Rossman Moore = The Basic Practice of Statistics by David S. Moore Freeman = Statistics, 2nd Edition by Freedman et al. Quantitative Literacy Series = Quantitative Literacy Series by David Freedman.

Unit 1: Exploring Data Distributions
Unit 2: Exploring Data Relationships
Unit 3: Designing Samples and Experiments
Unit 4: Sampling Distributions & Probability
Unit 5: Inferences from Data: Principles
Unit 6: Inferences from Data: Comparisons
Unit 7: Inferences from Data: Measurements
Unit 8: Inferences from Two Way Tables
Unit 9: Inferences for Regression
Unit 10:Review and Preparation for AP Test
Unit 1: Exploring Data Distributions

Time: 4 weeks
 Topic & Activities Resources 1. Data, Variables and Distributions Rossman - Topic 1 2. Displaying and Describing Distributions Rossman - Topic 2 3. Measures of Center Rossman - Topic 3 4. Measures of Spread Rossman - Topic 4 5. Comparing Distributions Rossman - Topic 5 6. Readings and Report Freedman - Chapter 4 7. Introduction to major project

Unit 2: Exploring Data Relationships

Time: 5 weeks
 Topic & Activities Resources 1. Graphical Displays of Association Rossman - Topic 6 2. Correlation Rossman - Topic 7 3. Least Square Regression Rossman - Topic 8 & 9 4. Interpreting Correlation & Regression Moore - Section 2.4 5. Meaning of Regression. Why Least Squares Bohan 6. Readings and Report Freedman - Chapters 8 & 10 7. Influential Points Activity Quantitative Literacy Series 8. Contingency Tables Rossman- topic 10 9. Major Project Work

Unit 3: Designing Samples and Experiments

Time: 4 weeks
 Topic & Activities Resources 1. Random Sampling Rossman - Topic 11 2. Readings and Report Freedman - Chapters 1 & 2 3. Sampling Distributions: Confidence Rossman - Topic 12 4. Sampling Distributions: Significance Rossman - Topic 13 5. Normal Distributions Rossman - Topic 14 6. Central Limit Theorem Rossman - Topic 15 7. Designing Experiments Rossman - Topic 20 8. Major Project Work

Unit 4: Sampling Distributions & Probability

Time: 3 weeks
 Topic & Activities Resources 1. Probability Distributions Moore - Section 4.2 2. Sample Proportions Moore - Section 4.3 3. Binomial Distributions Moore - Section 4.4 4. Sample Means Moore - Section 4.5

Unit 5: Inferences from Data: Principles

Time: 3 weeks
 Topic & Activities Resources 1. Confidence Intervals Rossman - Topics 16 & 17 2. Tests of Significance Rossman - Topics 18 & 19

Unit 6: Inferences from Data: Comparisons

Time: 2 weeks
 Topic & Activities Resources 1. Comparing Two Proportions Rossman - Topics 21 & 22 2. Major Project Work

Unit 7: Inferences from Data: Measurements

Time: 3 weeks
 Topic & Activities Resources 1. Inference for a Population Mean Rossman - Topics 23 & 24 2. Comparing Two Means Rossman - Topic 25 3. Major Project Work

Unit 8: Inferences from Two Way Tables

Time: 2 weeks
 Topic & Activities Resources 1. Two-Way Table-expectancies Moore - Chapter 8 2. The Chi-Squared Test Moore - Chapter 8 3. Readings and Report Freedman - Chapter 28 4. Major Project Work

Unit 9: Inferences for Regression

Time: 2 weeks
 Topic & Activities Resources 1. The Regression Model Moore - Chapter 10 2. Confidence Intervals for the Regression Slope Moore - Chapter 10 3. Testing Hypothesis of Non-Linear Relationship Moore - Chapter 10 4. Major Project Work

Unit 10: Review and Preparation for AP Test

Time: 2 weeks
 Topic & Activities Resources ---- ---

The choice of presenting small sample methods prior to large sample methods reflects the treatment of the topics in Rossman's text. This ordering has been approved in consultation with Alan Rossman.

Instruction on technology, with particular emphasis on the TI-83 and Minitab, is incorporated into the pursuit of the regular class activities. Some allowances in the time schedule for the early units have been made to accommodate direct instruction within the context of an assigned activity.

## Teaching Strategies

This course is organized as an activity based experience for the students. Lecture is held to the minimum with the students actively engaged in discovery and exploration of statistical realities and relationships. This design is consistent with the constructivist philosophy of education. The teacher attempts to facilitate and guide the student's explorations and formations of hypotheses. Students learn appropriate statistical techniques within the context of statistical activities and experiences better than they can learn from lecture-based teaching of the techniques.

The discovery and exploration are fully supported with technology, particularly the TI-83 calculator and secondarily Minitab statistical software. Students are required to have graphing calculators with a full menu of statistical functions; the Mathematics Department does not require any particular brand or model of calculator. However, mathematics teachers at our school tend to prefer either the TI-83 or TI-85.

Much of the course is devoted to developing the students into competent interpreters and investigators of statistical data and information. The activities of decision making and validating/justifying statistical hypotheses are of the highest importance. The goal is to develop competent users and receivers of statistical information; consequently, proof and algebraic justification are restricted to topics for which it has been determined that such activities will serve to deepen the understanding of the students and further empower them in statistics.

Our choice of Workshop Statistics: Discovery with Data (Rossman, 1996) supports this approach to learning. As the Preface states,
This book contains activities that guide students to discover statistical concepts, explore statistical principles, and apply statistical techniques. Students work toward these goals through the analysis of genuine data and through interactions with each other, their instructor, and with technology.

## Major Projects

Each student is to conduct a major project throughout the entire course. This major project involves a substantial set of bivariate data on which the students will apply all of their statistical techniques and concepts. Students are encouraged to begin the project with real data from their own experience. Suggested sources of data include data that student's parents or guardians have, school data (with proper safeguard for confidentiality), statistical abstracts, etc. Students are instructed that one of the components of the project is to evaluate their data: this evaluation may determine that the data set is not usable. Should this occur, students will have to gather more data in order to proceed with this component of the course. It is our belief that the experience of this project should parallel real-world statistical practice.

During the term of the project, each student will analyze each component of their data set, investigate relationships between the components, use the components as the superset for random sampling activities and the basis for hypothesis testing and
interpretation.

## After the AP Test

Once the AP Test has been administered, the students explore a variety of statistical topics including an Introduction to Analysis of Variance and other regression models. Time is also devoted to polishing each student's Major Project report.

## Assessment

The assessment program for AP Statistics has two components:

1. Each Nine Week Marking Period:
a) Homework activities are assigned each class and are not graded. They are discussed extensively in class.

b) Quizzes deal with the full range of procedures and interpretations for each topic.

c) Tests are administered at the end of each unit. The tests cover both concepts and techniques and include AP Statistics type questions as much as possible. Questions include both short answer skill and conceptual items as well as more extensive multi-step analyses and interpretations of analyses.

d) Readings and Reports are assigned independently of the normal class work. Students are to submit a brief written report for each of the assignments.

e) Major Project evaluation will occur at the end of each 9 week marking period. The project is graded according to how well the student applies of the concepts and techniques of that marking period.

2. At the end of each semester, a Semester Examination will be administered. This test is designed to assess the more global and interpretative aspects of the curriculum.

a) The Marking Period Grade is the mean of the all tests of the marking period. The mean of the quizzes is used as one test. The evaluation of the Major Project is calculated in the following way:
i) 1st and 2nd Marking Periods: worth one test

ii) 3rd and 4th Marking Periods: worth two tests
The Marking Period Grade is adjusted based on the discussion as part of the Competency Based Grading System (see below).

b) The Semester Grade is calculated using the following weights:
i) Each Marking Period grade: 40%

ii) Semester Examination: 20%

Competency Based Assessment

1. At the beginning of the course, each student is presented with a list of competencies (see page 10) for AP Statistics. At the end of each unit, the teacher makes a judgment regarding the status of competencies that were addressed during that unit. The categories of evaluations are Excellent (97), Proficient (92), Adequate (85), Marginal (78) and Unsatisfactory (65). Each student's Competency List is then updated by entering the date of the evaluation in the appropriate column.

2. Each Competency Grade is subject to revision at any time throughout the balance of the course. Revision is accomplished either by administration of a retest of that competency or by the presentation of evidence by the student in a conference with the
teacher. This second option is by far the more popular and provides the beneficial requirement that the student must argue for an increase in rating. In addition, a rating may move down if the teacher perceives that the performance of a particular
competency has slipped.

3. At the end of each Marking Period, the ratings are quantified.

4. Each student then has a conference with the teacher at which time the two evaluations, traditional and competency-based, are reconciled The student and teacher come to an agreement regarding the letter grade that best represents the student's level of understanding and performance and that will be reported to the school. This negotiation session has proved most beneficial in our school's AP Calculus courses.

## Resources

Primary:

• Allan J. Rossman, Workshop Statistics: Discovery With Data. New York, NY: Springer-Verlag New York, Inc., 1996.
• David S. Moore, The Basic Practice of Statistics. New York, NY: W. H. Freeman and Company, 1995.

Secondary:

• David Freedman, Robert Pisani, Roger Purves, Ani Adhikari, Statistics, 2nd Edition. New York, NY. W. W. Norton & Company, 1991.
• Gnanadesikan, Landwehr, et al., Quantitative Literacy Series: Exploring Data, Exploring Probability, The Art and Technique of Simulation, Exploring Surveys and Information from Samples, Exploring Measurements. Palo Alto, CA. Dale Seymour Publications, 1986.

### Competency Chart

 Competency Chapt. Exc Prof Adeq Marg Unsat Calculation and interpretation of summary statistics Construction and interpretation of graphical displays of univariate data: dotplot, stem plot, histogram, box plot. Comparing distributions of univariate data graphically: back-to-back stem plots, parallel histograms, multiple box plots Application and interpretation of z scores Construction and interpretation of graphical displays of bivariate data: scatter plots, regression lines, residual plots, outliers, and influential points Meaning of and calculation formula for correlation coefficient. Meaning of and derivation of least squares line. Transformations to produce linearity. Types of studies, experimental design Random sampling: concept and strategies Controlling for bias and sampling error Elementary probability theory; probability as relative frequency Elementary probability theory; probability as relative frequency Simulations with probability distributions Concepts and application of the Normal Distribution Sampling distributions: sample proportion, sample mean, difference between two sample proportions, difference between two sample means Central Limit Theorem Confidence Intervals: meaning and techniques * Analyzing categorical data: graphically and with the Chi Square Distributions Inference for regression

* major topics - competency rating calculated with twice the weight of other categories