Advanced Placement Statistics
AP Statistics is an introductory college-level statistics course that introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students cultivate their understanding of statistics using technology, investigations, problem solving, and writing as they explore concepts like variation and distribution; patterns and uncertainty; and data-based predictions, decisions, and conclusions.
Overview
Most classes will be broken into a lecture portion and a classwork portion. The classwork will pertain to the lecture just given. Classwork will often involve a combination of hand written work, results collected from calculator and computer program output, and visual aids, such as news programs and articles that involve applications of statistics.
At the end of each class, reading from the textbook will be assigned. The student is expected to complete the reading by next class.
Each week, homework from the textbook and other sources will be assigned. Homework will be collected every Monday.
Each week, a project will be assigned that involves creating and interpretting statistical graphs, performing analysis on real-life data sets, simulating outcomes using random numbers or other applications. Usually, projects will be covered in detail on Friday classes; the student will have time in class on Friday to begin the project and then it will be due the following Monday. Projects will be uploaded to the Google Classroom Assignments tab.
Course Content
This course will provide the student with a toolset to design scientific experiments, test hypotheses, collect data and then draw conclusions from said data using the principles of probability and statistics.
Over the school year, the student will study concepts such as sampling distributions, random variables and expectations. They will become acquainted with the ideas of chance and likelihood . In doing so, they will come to understand how uncertainty affects decision-making. They will see the effects of uncertainty in the estimation of population parameters from sample data.
The student will learn how to describe and see the effects of uncertainty in the shape and distribution of data. The student will become skilled in identifying features like skewness, outliers and normality .
To accomplish this, the student will be taking a look at many datasets drawn from everyday life. Among the datasets the student will examine,
The student will use a combination of technology to analyze these datasets. The activities in the class will explore, among other things,
The effects on bias on distribution shapes
Constructing sampling distributions
How to test hypotheses using control groups
Identifying correlation in bivariate data and utilizing it to make predictions
Simulating random outcomes to visualize the Law of Large Numbers
Topic Outline
Unit 1 (Starnes and Tabor): Exploring One-Variable Data
Unit 2 (Starnes and Tabor): Exploring Two-Variable Data
Unit 3 (Starnes and Tabor): Collecting Data
Chapter 1 (From Contemporary Mathematics Textbook): Set Theory
Chapter 7 (From Contemporary Mathematics Textbook): Probability
Unit 4: Probability, Random Variables, and Probability Distributions
Chapter 6 (From Introductory Statistics Textbook): Normal Distribution
Chapter 7 (From Introductory Statistics Textbook): The Central Limit Theorem
Unit 5 (Starnes and Tabor): Sampling Distributions
Unit 6 (Starnes and Tabor): Inference for Categorical Data: Proportions
Unit 7 (Starnes and Tabor): Inference for Quantitative Data: Means
Unit 8 (Starnes and Tabor): Inference for Categorical Data: Chi-Square
Unit 9 (Starnes and Tabor): Inference for Quantitative Data: Slopes
Project Overview
Below, some of the projects that will be completed by the student are broken down by unit.
In Unit One, the student will examine categorical frequency distributions and the relationship between different categorical variables using the Electric Vehicles Registered in Washington State dataset. They will also examine distribution shapes with histograms and learn how to detect outlying observations using datasets such as Old Faithful Eruption Times , and the Length of Roman Emperor Reigns
In Unit Two, the student will study and visualize the correlation in datasets such Celebrity Twitter Data , the Challenger Shuttle Explosion and others. They will use this correlation to find the line of best fit and then use the linear regression equation to make predictions. In the process, they will learn to interpret the meaning of residuals and to assess whether the distribution of residuals provides evidence of a model fit.
In Unit Three, the student will learn how to detect and prevent bias using the Vietnam Draft Data dataset. They see first hand how bias can lead to real world consequences.
In Unit Four, the student will create simulations of random variables using software to generate random numbers. Through this, they will become acquainted with the patterns that can be found even in random events. They will learn about pseudo random numbers. They will learn how to use random numbers to construct theoretical probability distributions.
In Unit Five, the student will take the idea of simulation and use it to demonstrate the Central Limit Theorem. In the process, the student will construct theoretical sampling distributions to see how the Central Limit Theorem arises naturally from random variation. After learning about the Central Limit Theorem, they will use it to calculate confidence intervals for population parameters based on point estimates.
In Units Six - Nine, the student will apply statistical reasoning to determine whether sufficient evidence can be found in a sample of data to draw conclusions. They will set up null and alternate hypotheses, calculate test statistics and apply statistical inference. They will learn how to interpret the results of their inferences in terms of statistical significance . To do so, the student will examine datasets such as Avocado Prices , Diamond Prices , Marvel Movies , among many others.
In addition, if time permits, the following topics will be covered:
the student will learn how to apply Monte Carlo Simulation to model financial outcomes
the student will interact with machine learning programs to see how linear regression is applied in the real world.
Text
Reading will be assigned from The Practice of Statistics (for the AP Exam) by Daren S. Starnes and Josh Tabor (ISBN: 9781319113339), 6 th edition. This textbook will distributed to students on the first day of class. It expected the students will bring the textbook to class every day. Most, but not all (see next paragraph), reading and homework be will assigned from this textbook.
Several units of this text will be supplemented with chapters from an online textbook library, OpenStax . We be using the Contemporary Mathematics textbook and the Introductory Statistics textbook at several points in the class. Reading and homework will be assigned from these textbooks at various points in the class.
We will be using Chapter 1: Set Theory and Chapter 7: Probability from the Contemporary Mathematics textbook when we cover Unit 4 from the Starnes & Tabor textbook.
We will be using Chapter 6: Normal Distribution and Chapter 7: The Central Limit Theorem from the Introductory Statistics textbook when we cover Unit 5 from the Starnes & Tabor textbook.
We will be using Chapter 8: Confidence Intervals from Introductory Statistics when we cover Unit 6 and Unit 7 from the Starnes & Tabor textbook.
The online Class Notes
Technology
TI-84 The student is expected to bring a calculator from the TI-84 series of calculators to class every day. It is important the calculator is a TI-84 and not one of the older TI-83 . TI Connect CE will be used to transmit datasets to students during class. This software will only integrate with calculators from the TI-84 series.
ChromeBook The student is expected to bring the ChromeBook they have been provided to class every day. It should be fully-charged. The student will need this to access online resources such as projects and datasets.
Python 3 Students will be shown how to install Python3 on their ChromeBooks very early in the class schedule. Python 3 will be used to perform data analysis and generate graphical representations of data. Statistical graphs will be generated using matplotlib .
All projects and some class work will be done Python 3 . In each case, the student will write programs that perform statistical analysis and interpret the results.
Google Classroom
Any and all announcements will be posted to the Google Classroom. Any assignments or projects that are completed on the student’s ChromeBook will be uploaded to Google as zip files. The code to join the classroom is given below,
Classroom Code Will be distributed on the first class date.
Website
All of the class notes, classwork, homework and projects for this class can be found at https://bishopwalshmath.org/ . This site includes references to additional resources, such as datasets used in class, tutorial videos and links to relevant Python documentation.
NOTE : I will probably change the address to “https://apstats.bishopwalshmath.org ” once I have everything setup.
Grading Breakdown
Area
Percentage
Quizzes
10%
Exams
25%
Homework
25%
Classwork
20%
Projects
20%
Quizzes
Quizzes will be of the pop variety, meaning they will not be announced ahead of time. Quizzes will typically be short, five to ten minutes assessments aimed at verifying reading selections have been read by the student before class begins.
Class Notebook
The student is expected to bring their own notebook to take notes during class. This notebook is separate from the classwork notebook and homework notebook; it belongs to the student and will not be collected for grading.
While students will use their ChromeBooks extensively in class to perform data analysis, when these activities are not being done, it is expected the ChromeBook will be closed and all note-taking will occur in the student’s notebook.
Projects
The student will complete projects using their ChromeBook and Python 3 . The projects will involve performing analysis on data sets, visualizing results and interpretting the output.
Projects will include either one or several .csv files and a .py script file. The .py file will contain a Python 3 program written by the student that addresses and answers all assigned exercises. Written responses will be included in comments in the script files.
Projects will be zipped into zip files and uploaded to Google.
The student will be shown how to do all of this in class before the first project is assigned.
Exams
The topics covered on each exam are listed below, along with their tentative dates. Unless otherwise noted, all chapters come from the Starnes & Tabor textbook.
Exam 1: September 29 th
Exam 2: December 8 th
Chapter 1 (From Contemporary Mathematics Textbook): Set Theory
Chapter 7 (From Contemporary Mathematics Textbook): Probability
Unit 4: Probability, Random Variables and Probability Distributions
Exam 3: Februrary 9 th
Chapter 6 (From Introductory Statistics Textbook): Normal Distribution
Chapter 7 (From Introductory Statistics Textbook): The Central Limit Theorem
Unit 5: Sampling Distributions
Exam 4: April 5 th
Chapter 8 (From Introductory Statistics Textbook): Confidence Intervals
Unit 6: Inferences for Categorical Data - Proportions
Unit 7: Inferences for Quantitative Data - Means
Final: Last Day of Class