Course Title: Advanced Placement Statistics
Meeting Times: This course runs for 36 weeks and meets every second day. Each period consists of 80 minutes of instructional time.
Course Description:
AP Statistics provides a systematic development of the concepts, principles, and tools of statistics with an emphasis on inquiry and critical-thinking skills associated with the collection, representation, analysis, and drawing conclusions from authentic data. Topics of study include data investigation, designing and conducting studies, anticipating patterns using probability and simulations, and statistical inference. Technology is a central component of the course and includes the use of graphing calculators, computers, and data analysis software. On a regular basis, graphing calculators and computers are used to explore, discover, and reinforce concepts of statistics and probability.
Though our system has an open enrollment policy, students should understand that this course is designed to be a fourth-year mathematics course, and the equivalent of an introductory, one-semester, non-calculus-based, college-level statistics course. The course requires a working knowledge of Algebra II, and quantitative reasoning. The breadth, pace, and depth of material covered exceeds the standard high school mathematics course, as does the college-level textbook, and time and effort required of students. This course provides the statistics foundation for college majors in social sciences, health sciences, and business, and serves as the preparation for an upper-level, calculus-based statistics course for majors in the sciences, engineering, and mathematics. Students are expected to take the AP Statistics Exam at the end of this course.
Course Purpose and
Goals:
Philosophy
Understanding statistics as the science of data is the basis of this course. Statistics is the formal study of data as numbers in a context. Students build an understanding of statistical concepts as they construct relationships and make connections among the various representations of data and how data is interpreted. The course is more than a collection of topics; it is a coherent, focused curriculum that develops a broad range of statistical and probabilistic thinking, and a variety of statistical methods and applications. Although the development of techniques and fluency with graphic and numeric representations to represent problems is important, it is not the only focus of the course. Rather, the course emphasizes a conceptual development of statistical thinking through the use of an exploratory analysis of real data often using technology, planning and implementing well-designed studies, and engaging students in active learning. According to the National Council of Teachers of Mathematics (2000), "The amount of data available to help make decisions in business, politics, research, and everyday life is staggering… Statistics are often misused to sway public opinion on issues or to misrepresent the quality and effectiveness of commercial products. Students need to know about data analysis and related aspects of probability in order to reason statistically—skills necessary to becoming informed citizens and intelligent consumers" (p. 48).
To support students’ development of statistical thinking, technology is used to enhance their understanding of major concepts and tools for working with data. The College Board requires the use of graphing calculators for this course. Mathematical problem solving, investigations, and projects require adequate and timely access to technology including graphing calculators, databases, spreadsheets, Internet and on-line resources, and data analysis software packages. In this course, technology is introduced in the context of real-world problems, incorporates multiple graphical representations, uses a simulation approach for studying probability, and facilitates connections to other disciplines. Students actively participate in the process of statistical investigations by using estimation, mental math, calculators, computers, and paper-and-pencil techniques.
The standards support the unifying themes of exploring
data, sampling and experimentation, anticipating patterns, and statistical
inference. Instruction is designed and sequenced to provide students with
learning opportunities in appropriate settings. Teaching strategies include collaborative small-group work, pairs
engaged in data analysis, whole-group presentations, peer-to-peer discussions,
and an integration of technology when appropriate. In this course, students are
often actively engaged in statistical investigations that enable them to
collaborate with peers in fitting mathematical models to the data and interpret
how well the model fits the data. It is a cyclic process in which the data
suggest refinements in original questions and mathematical models used. Based
on the data, relationships among variables are evaluated through appropriate
methods of analysis. Students are encouraged to discuss the mathematics of
statistical analysis and inferences, to use the language and tools of
statistics to communicate, and to discuss problems and methods of solution.
Goals
Students should be able to:
1. Develop statistical thinking based on a conceptual understanding of major topics and tools of data collection, representation, analysis, inference, and conclusions.
2. Analyze and interpret data from graphical displays and numerical distribution summaries, and justify conclusions.
3. Employ the language and symbols of statistics, and effectively communicate the formulation of questions, data collection methods and displays, interpretation of statistical analysis, and evaluation of inferences and predictions based on the data.
4. Use probability as a tool to predict how the distribution of data is related to an appropriate mathematical model.
5. Develop an understanding of statistical inference through the use of confidence intervals and tests of significance.
6. Use graphing calculators and computers in the exploration, statistical analysis, simulation, and modeling of data.
7. Make sense of and evaluate the reasonableness of conclusions based on data.
8. Develop an appreciation for an historical perspective of statistics.
Conceptual Organization
The content and level of depth of the material for this course is equivalent to a college-level course. The course content is organized to emphasize major topics in the course to include the following: (1) exploring data, (2) sampling and experimentation, (3) anticipating patterns, and (4) statistical inference. Building on most students’ prior knowledge, the course begins with a review of graphical and numerical data displays. Technology enhances students’ constructing an understanding of mathematical relationships among these different representations used in solving problems. This supports and leads to students’ visualization and discussion of distribution summaries including measures of center, spread, and position. Information from distributions of univariate data are compared and interpreted in the context of real-world problems. Normal distributions are examined prior to moving to the study of bivariate data.
Students are provided with opportunities to generate and collect bivariate data, and they analyze relationships between variables using scatter plots, linear correlations, and least squares regression lines. Outliers, influential points, residual plots, and transformations to achieve linearity are examined. This is followed with a focus on the concept of cause and effect, confounding variables, and relationships found in categorical data. In quarter 2, students investigate the purpose and process of a statistical investigation. The concept of randomness is studied and a variety of data collection methods that are used to support the design of a well-planned study. This naturally leads to an examination of sampling error and sources of bias. Probability is introduced as a method for exploring random phenomena, used to analyze simulations, and viewed as predictable patterns in sampling distributions. Specifically, students begin to work with binomial and geometric distributions and probabilities near the end of the first semester.
During the second semester of the course, students broaden their understanding of statistical concepts and techniques to include more sampling distributions, the Central Limit Theorem, and statistical inference. Confidence intervals and tests of significance are emphasized through a wide-range of appropriate models dependent upon the conditions of particular real-world problems. This order of topics within the course, not only provides a logical and systemic study to calculus, but also accommodates the frequent transfer of students within the schools of the system, so that transfer students can maintain a consistent flow of learning.
Course Format and
Policies:
A typical class format consists of
Grading policy consists of tests for every chapter (60%), assignments or short projects (15%) and homework completed (25%). At the end of Semester 1, there will be a final exam. At the end of Semester 2, there will be a final exam and also the students will have to present research done over the last month of classes.
Homework policy: The purpose is to practice the skills learned from day to day. Students can expect to have homework daily. It is the student’s responsibility to stay caught up and review their work regularly. Homework assignments for the entire year are passed out the first week of class. If an unplanned absence occurs, the students should get the notes from another student and work on the assignments. The instructor will review the homework given out on a daily basis.
Weighted grades are calculated for students completing and taking the requisite exam of an AP course.
Unweighted Scale A=4 Weighted Scale A=5
Unweighted Scale B=3 Weighted Scale B=4
Unweighted Scale C=2 Weighted Scale C=3
Unweighted Scale D=1 Weighted Scale D=2
Unweighted Scale F=0 Weighted Scale F=1
Textbook, Materials
and Other Resources:
Required Textbook
Supplemental Textbooks and Readings
Other Resources
Course Content Outline:
Each major theme has the following percentage of:
Semester 1:
Semester 2
|
Unit |
Quarter |
Week |
Topics |
Learning tools |
Assessments |
|
I. Organizing Data Make
· use of graphical and numerical techniques to study data; ·
interpretation from graphical and numerical displays
and summaries. |
|
|
|
|
|
|
Chapter
1 Exploring
Data 1.1 Displaying
Distributions with Graphs 1.2 Describing
Distributions with Numbers |
1 |
1-3 |
·
Dotplots, stemplots,
and histograms ·
New coverage of ogives
and linear transformations ·
Mean, median, spread,
outliers ·
Five number summary ·
Boxplots ·
Variance, standard
deviation ·
Linear transformation |
Many
new examples and exercises using contemporary, real data Homework Use
of the calculator to find the five number summary, variance and standard
deviation Use
of the graphing calculator to draw boxplots. |
Test
1 Multiple
Choice, Problems, Constructed Response |
|
Chapter
2 Normal Distributions 2.1 Density Curves and the
Normal Distribution 2.2 Standard Normal
Calculations |
1 |
4-5 |
·
Density curves and
standard deviation ·
68 – 95 - 99.7 rule ·
Standard normal
distribution (Z) ·
Z – table ·
Normal probability
plot |
Project:
Normal distribution with a dart board; demonstrate and calculate normal
distribution with every day life activities Examples
done in class Use
of the calculator to find the normal distribution |
Project
with the dart board Test
2 Multiple Choice, Problems, Constructed Response |
|
Chapter 3 Examining
Relationships 3.1 Scatterplots 3.2 Correlation 3.3 Least-Squares
Regression |
1 |
6-7 |
·
Scatterplot:
explanatory and response variable, linear relationship, strength ·
Correlation r ·
Least square
regression line ·
Residuals ·
Influential
observations |
Project:
Relation between body part of different people; finding the correlation
between people Use
of the calculator to draw scatterplots, calculate the correlation, least
square regression line Useof the computer to analyze data |
Project
with the body parts. Test
3 Multiple Choice, Problems, Constructed Response |
|
Chapter 4 More
on Two-Variable Data 4.1 Transforming
Relationships 4.2 Cautions about
Correlation and Regression 4.3 Relations in
Categorical Data |
1 |
8-9 |
·
Transformation of
scale using logarithm ·
Exponent growth and
power law model ·
Causation, common
response, confounding ·
Two-way table ·
Simpson’s paradox |
Project:
Cancer spreading; finding the mathematical model of a cancer simulation Use
of the calculator to draw line graph, change to logarithm scale Use
of the computer to perform scale transformation with different relations |
Project
about the cancer Test
4 Multiple Choice, Problems, Constructed Response |
|
II. Producing Data Method
of data collection and analysis. |
|
|
|
|
|
|
Chapter 5 Producing data 5.1 Designing Samples 5.2 Designing Experiments 5.3 Simulating Experiments |
2 |
10-11 |
·
Methods of data
collection: census, sample survey, experiment, observational
study ·
Sampling methods · Treatments, experimental
units · Simulation |
Project:
Farmer’s field: different sampling methods to analyzed which one works best Use
of the calculator to create simulations |
Project
about sampling Test
5 Multiple Choice, Problems, Constructed Response |
|
III. Probability Anticipating
what the distribution of data should look like. |
|
|
|
|
|
|
Chapter 6 Probability:
The study if randomness 6.1 The Idea of
Probability 6.2 Probability Models 6.3 General Probability
Rules |
2 |
12-13 |
·
Sample space ·
Probability model ·
Complements ·
Disjoint, independent
and dependant events |
Hands-on
activities with probability games |
Test
6 Multiple Choice, Problems, Constructed Response |
|
Chapter 7 Random
Variables 7.1 Discrete and
Continuous Random Variables 7.2 Means and Variances of
Random Variables |
2 |
14-15 |
·
Probability distribution ·
Discrete random
variable ·
Continuous random
variable ·
Density curve (normal
distribution) ·
Mean and variance ·
Transformation
combining two variables |
Use
of the calculator to perform calculation from the probability distribution Use
of the computer to simulate probability distribution |
Test
7 Multiple Choice, Problems, Constructed Response |
|
Chapter 8 The
Binomial and Geometric Distributions 8.1 The Binomial
Distributions 8.2 The Geometric
Distributions |
2 |
16-17 |
·
Binomial coefficient ·
Factorial ·
Binomial probability ·
Geometric probability |
Project:
Binomial and geometric distribution using dice. Calculate and experiment
using dice. |
Project
with the dice Test
8 Multiple Choice, Problems,
Constructed Response |
|
|
2 |
18 |
Review for Semester Exam |
|
Semester 1 Assessment Multiple Choice, Problems,
Constructed Response |
|
Chapter 9 Sampling
Distributions 9.1 Sampling Distributions 9.2 Sample Proportions 9.3 Sample Means |
3 |
19-20 |
·
Population proportion ·
Mean and standard
deviation of the sampling distribution of p ·
Central limit theorem |
Class
simulation with normal distribution |
Test
9 Multiple Choice, Problems, Constructed Response |
|
IV. Inference Statistical
inference guides the selection of appropriate models. |
|
|
|
|
|
|
Chapter 10 Introduction
to Inference 10.1 Estimating with
Confidence 10.2 Tests of Significance 10.3 Making Sense of
Statistical Significance 10.4 Inference as Decision |
3 |
21-23 |
·
Confidence interval ·
Confidence interval
for the mean m ·
Margin of error ·
Ho one and two sided alternative ·
P - values ·
Introduction of Inference
Toolbox ·
Expanded treatment of
Type I, Type II errors and Power |
Use
of the calculator to perform calculation |
Test
10 Multiple Choice, Problems, Constructed Response |
|
Chapter 11 Inference
for Distributions 11.1 Inference for the
Mean of a Population 11.2 Comparing Two Means |
4 |
24-25 |
·
Tests and confidence
intervals for the mean m of a normal population ·
t table ·
Confidence interval ·
Significance test ·
Increased emphasis on
distinguishing matched-pairs from two-sample procedures |
Use
of the calculator to perform calculation Use
of the t table to calculate the confidence interval |
Test
11 Multiple Choice, Problems, Constructed Response |
|
Chapter 12 Inference
for Proportions 12.1 Inference for a
Population Proportion 12.2 Comparing Two
Proportions |
4 |
26-27 |
·
z procedure ·
Confidence interval ·
Choosing the sampling
size ·
Derivation of the mean
and standard deviation of the sampling distribution of p1 and p2 |
Use
of the calculator to perform calculation Use
of the F distribution critical values table |
Homework Test
12 Multiple Choice, Problems, Constructed Response |
|
Chapter 13 Inference
for Tables: Using Chi-square 13.1 Test for Goodness of
Fit 13.2 Inference for Two-Way
Tables |
4 |
27-28 |
·
Chi-square
distribution with n-1 degrees of freedom ·
Chi-square statistics ·
Performing Chi-square
test |
Use
of the calculator to perform calculation Use
of the Chi-square distribution table |
Test
13 Multiple Choice, Problems, Constructed Response |
|
Chapter 14 Inference
for Regression 14.1 Inference about the
Model |
4 |
29-31 |
· Regression model · True regression line · Standard error about the line s |
|
Quiz
14.1 |
|
|
4 |
32 |
· Review for Semester Exam |
|
Semester
2 Assessment Multiple
Choice, Problems, Constructed Response |