Advanced Placement Statistics Syllabus
Course Design
This AP Statistics course is taught as a non-calculus-based, activity-driven course in which students actively
construct their own understanding of the concepts and methods of statistics. Students explore the realms of
descriptive and inferential statistics. The major conceptual themes studied are “Exploring Data,” “Planning
and Design of a Study,” “Anticipating Patterns,” and “Statistical Inference”, as outlined by the College
Board.
Technology, with particular emphasis on the TI-83+, TI-84, TI-89 calculators and Fathom and Minitab
software, is incorporated into the regular class activities.
The course also employs research on real-world data and newspaper/online journal research to promote
student awareness of statistical concepts and judgments in the world around them.
Pre-requisites for the course, unit concepts, textbook and resource usage, technology adaptation, teaching
strategies, and assessments are designed to suit the College Board’s AP Statistics Course Description.
Primary Textbook*
Peck, Roxy, Chris Olsen, Jay Devore. Introduction to Statistics and Data Analysis. Belmont, CA:Thomson
Brooks/Cole, 2001 (This book is referenced as POD in this document)
Supplemental Textbooks
Bock, David E., Paul F. Velleman, and Richard D. DeVeaux. Stats: Modeling the World. Boston:
Pearson/Addison-Wesley, 2004.
Moore, David S. and George P. McCabe. Introduction to Practice of Statistics, 4th edition (or later). New
York: W.H. Freeman Co., 2003.
Watkins, Ann, Richard Scheaffer, and George W. Cobb. Statistics in Action: Understanding a World of
Data. Emeryville, CA: Key Curriculum Press, 2004.
Yates, Daniel S., David S. Moore, and Daren S. Starnes. The Practice of Statistics. New York: W.H.
Freeman, 2003.
Yates, Daniel S., David S. Moore, and Daren S. Starnes. The Practice of Statistics. New York: W.H.
Freeman, 1999.
Course Outline
The following is an outline of the major topics covered by the AP Examination in Statistics. The course
provides instruction in each of the following four broad conceptual themes outlined in the AP Statistics
Course Description with appropriate emphasis on each:
I. Exploring Data: Describing patterns and departures from patterns (20%-30%)
Exploratory analysis of data makes use of graphical and numerical techniques to study patterns and
departures from patterns. Emphasis should be placed on interpreting information from graphical and
numerical displays and summaries.
II. Sampling and Experimentation: Planning and conducting a study (10%-15%)
Data must be collected according to a well-developed plan if valid information on a conjecture is to
be obtained. This plan includes clarifying the question and deciding upon a method of data collection
and analysis.
III. Anticipating Patterns: Producing models using probability theory and simulation (20%-30%)
Probability is the tool used for anticipating what the distribution of data should look like under a
given model.
IV. Statistical Inference: Estimating population parameters and testing hypotheses (30%-40%)
Statistical inference guides the selection of appropriate models.
Chapter
from
POD*
and
approx.
Time
Chapter title
from
POD*
text
AP Statistics Topic
Covered
Intro to Statistics
Statistics and Data
Analysis
1&2
2 weeks
The nature and role
of Variability
II A Overview of methods of data
collection
1. Census
2. Sample survey
3. Experiment
4. Observational study
II B Planning and conducting surveys
1. Characteristics of a well-designed
and well-conducted survey
2. Populations, samples, and random
selection
3. Sources of bias in sampling and
surveys
4. Sampling methods, including
simple random sampling, stratified
random sampling, and cluster
sampling
Resources and
Activities
1st 6 weeks project:
Vocabulary in action
TI-83 Enhanced
Statistic
Calculator Activities
(completed at various
points throughout the
year)
Article taken from
http://apcentral.colle
geboard.com on AP
exam format and
acceptable calculator
list, etc
http://apcentral.colle
geboard.com/membe
rs/article/1,3046,152171-0-8357,00.html
Correlation and
Causation
Recommend
ed Exercises
from POD*
text
Read pp. 1-10
p.6: 1.3 – 7
Types of Data
The Data Analysis
Process
Collecting Data
Sensibly:
Observation and
experimentation
II C Planning and conducting
experiments
1. Characteristics of a well-designed
and well-conducted experiment
2. Treatments, control groups,
experimental units, random
assignments, and replication
3. Sources of bias and confounding,
including placebo effect and blinding
4. Completely randomized design
5. Randomized block design,
including matched pairs design
3
2 weeks
Read pp. 11-26
p. 14: 2.1-4
p. 20: 2.5, 7, 8
II D Generalizability of results and
types of conclusions that can be drawn
from observational studies,
experiments, and surveys
Sampling
Simple
comparative
Experiments
Displaying
Categorical Data:
Frequency
Distributions, Bar
Charts, and Pie
Charts
Displaying
Numerical Data:
Dotplots and Stemand-Leaf Displays
Displaying
Numerical Data:
Frequency
Distributions and
Histograms
Interpreting the
Results of
Statistical Analyses
http://www.cut-theknot.org/do_you_kno
w/misuse.shtml
Random Rectangles
I A. Constructing and interpreting
graphical displays of distributions of
univariate data (dotplot, stemplot,
histogram, cumulative frequency plot)
1. Center and spread
2. Clusters and gaps
3. Outliers and other unusual
features
4. Shape
I C. Comparing distributions of
univariate data (dotplots, back-to-back
stemplots, parallel boxplots)
1. Comparing center and
spread: within group,
between group variation
2. Comparing clusters and gaps
3. Comparing outliers and other
unusual features
4. Comparing shapes
I E Exploring categorical data:
frequency tables
4. Comparing distributions using bar
charts
“Getting to Know
You” Questionnaire
The Game of Greed
Read pp. 27-35
p. 26: 2.11-21
odd
Read pp.
p. 35: 2.23-39
odd
p. 54: 3.2, 7
p. 62: 3.12-19
p. 79: 3.21, 23,
26, 27, 31, 34
Quantitative Data
project (sampling
and describing
distributions)
p. 33: 3.40-42,
45, 49, 50
4
2 weeks
5
2 weeks
Describing the
Center of a Data
Set
Describing
Variability in a
Data Set
I B. Summarizing distributions of
univariate data
1. Measuring center: median, mean
I B Summarizing distributions of
univariate data
2. Measuring spread: range,
interquartile range, standard deviation
Summarizing a
Data Set: Box Plots
I B Summarizing distributions of
univariate data
Interpreting the
Center and
Variability:
Chebyshev's Rule,
the Empirical Rule,
and z scores
Interpreting the
Results of
Statistical
Analyses:
ScatterPlots
p. 110: 4.2, 3, 5,
14
p. 120: 4.20, 22,
25
p. 125: 4.29-34
http://en.wikipedia.or
g/wiki/SAT
and
http://en.wikipedia.or
g/wiki/Iq
I D Exploring bivariate data
1. Analyzing patterns in scatterplots
p. 150: 5.1-8
Correlation and
Linearity
I D Exploring bivariate data
2. Correlation and linearity
p. 163: 5.9, 1214, 16-20
Fitting a Line to
Bivariate Data
I D Exploring bivariate data
3. Least squares regression line
monopoly game
activity
p. 174: 5.26-29,
32-35
Assessing the Fit of
a Line
I D Exploring bivariate data
4. Residual plots, outliers, and
influential points
I D Exploring bivariate data
5. Transformations to achieve
linearity: logarithmic and power
transformations
Reading Computer
Outputs
p. 188: 5.37-41,
43, 47
2nd 6 weeks project:
Transformations
(APEX VS)
p. 206: 5.52, 54,
55, 58-59
Nonlinear
Relationships and
Transformations
Chance
Experiments
Definition of
Probability, Law of
Large Numbers
6
2 weeks
4. Using boxplots
5. The effect of changing units on
summary measures
I B Summarizing distributions of
univariate data
3. Measuring position: quartiles,
percentiles, standardized scores (zscores)
“How Fast is Your
Heart Beating?”
(YMS p. 4)
Basic Properties of
Probability
Conditional
Probability,
Independence
p. 233: 6.7-10,
12
III A Probability as relative frequency
1. Interpreting probability, including
long-run relative frequency
interpretation
2. Law of Large Numbers’ concept
III A Probability as relative frequency
3. Addition rule, multiplication rule,
conditional probability, and
independence
III B Combining independent Random
Variables
1. Notion of independence
versus dependence.
Three Coin Pony
Three Point, One
Point Game
p. 248: 6.14, 15,
17, 18, 20-23,
28
p. 259: 6.29-35
p. 267: 6.36-38,
43-45, 47, 48,
51
General Probability
Rules - Addition
Rule,
Multiplication Rule
Estimating
Probabilities
Empirically and
Using Simulation
Random Variables
Probability
Distributions for
Discrete and
Continuous
The Mean and
Standard Deviation
of a Random
Variable
Linear
Combinations
7
2 weeks
8
2 weeks
The Binomial and
Geometric
Distributions
The Normal
Distributions Properties and the
Use of Tables
Checking for
Normality Constructing
Normal Probability
Plots
Using the Normal
Distribution to
Approximate a
Discrete
Distribution
Statistics and
Sampling
Variability
Sampling
Distribution of a
Sample Mean
Sampling
Distribution of a
Sample Proportion
p. 280: 6.53-56,
58, 60-63
III A Probability as relative frequency
5. Simulation of random behavior
and probability distributions
Heads Up! Project
(simulation)
III A Probability as relative frequency
4. Discrete random variables and
their probability distributions,
including binomial and geometric
Casino Lab - Craps,
Roulette, Blackjack,
Monte's Dilemma,
etc.
III A Probability as relative frequency
6. Mean (expected value) and
standard deviation of a random
variable, and linear transformation of
a random variable
p. 309: 7.1, 5, 7
p. 314: 7.9, 11,
15, 19
p. 333: 7.28-32,
38-40
III B Combining independent random
variables
2. Mean and standard deviation for
sums and differences of
independent random variables
III A Probability as relative frequency
4. Discrete random variables and
their probability distributions,
including binomial and geometric
p. 344: 7.44, 45,
47, 49
p. 345: 7.50, 51,
54-56
p. 363: 7.59-67
odd; 68-72, 75;
62, 68-72, 75
III C The normal distribution
1. Properties of the normal
distribution
2. Using tables of the normal
distribution
3. The normal distribution as a
model for measurements
p. 381: 7.88-94
p. 409: 8.1-4, 79
III D Sampling distributions
2. Sampling distribution of a sample
mean
3. Central Limit Theorem
III D Sampling distributions
1. Sampling distribution of a sample
proportion
Rice Virtual Lab
(sampling
distribution of
sample means)
ESP Card activity
(sampling
distribution of
sample proportion)
p. 420: 8.14-17,
20, 23, 25, 26
p. 426: 8.27-29,
31-33
Point Estimation,
Confidence
Intervals
Large Sample
Confidence Interval
for a Proportion
9
2 weeks
Large Sample
Confidence Interval
for a Mean
10
2 weeks
Hypotheses and Test
Procedures, Errors in
Hypothesis Testing,
Power and
Probability of Type II
Error
Hypotheses Testing
for a Population
Proportion
Hypotheses Testing
for a Population
Mean
Difference
Between Two
Means
(Independent
Samples)
Difference
Between Two
Means (Paired
Samples)
11
2 weeks
Difference
Between Two
Proportions
IV A Estimation (point estimators and
confidence intervals)
2. Properties of point estimators,
including unbiasedness and variability
IV A Estimation (point estimators
and confidence intervals)
1. Estimating population parameters
and margin of errors
3. Logic of confidence intervals,
meaning of confidence level and
confidence intervals, and
properties of confidence intervals.
4. Large sample confidence interval
for a proportion
III D Sampling distributions
7. t-distributions
IV A Estimation (point estimators
and confidence intervals)
5. Large sample confidence interval
for a mean
IV B Tests of significance
1. Logic of significance testing, null
and alternative hypotheses; pvalues; one- and two-sided tests;
concepts of Type I and Type II
errors; concept of power
IV B Tests of significance
2. Large sample test for a proportion
Hill of beans activity
(confidence interval
for a proportion)
One sample
proportion
confidence interval
project
p.467 (9.34,
9.38, 9.45, 9.46,
9.47)
Prosecutor's Fallacy
Activity
p. 481 (10.4,
10.6)
DNA Fingerprinting
Activity
“Is One Side of a
Coin Heavier?”
IV B Tests of significance
3. Large sample test for a mean
III D Sampling distributions
5. Sampling distribution of a
difference between two independent
sample means
IV A Estimation (point estimators
and confidence intervals)
7. Large sample confidence interval
for a difference between two means
(unpaired and paired)
IV B Tests of significance
5. Large sample test for a difference
between two means (unpaired and
paired)
III D Sampling distributions
4. Sampling distribution of a
difference between two independent
sample proportions
IV A Estimation (point estimators
and confidence intervals)
6. Large sample confidence interval
for a difference between two
proportions
p. 452: 9.10-13,
16, 17, 19
Designing
experiments with
paper helicopters
project
p. 500 (10.22,
10.27, 10.28,
10.36)
12
2 weeks
13
2 weeks
4 weeks
μσπχ
14
1 week
15
1 week
Chi-Squared Tests
for Univariate
Categorical Data
Tests for
Homogeneity and
Independence In a
Two-Way Table
The Simple Linear
Regression Model
Inferences
Concerning the
Slope of a
Population
Regression Line
Checking Model
Adequacy
Review for the AP
Exam
AP Statistics Exam
Multiple
Regression
Analysis
Analysis of
Variance
IV B Tests of significance
4. Large sample test for a difference
between two proportions
III D Sampling distributions
8. Chi-square distribution
IV B Tests of significance
6. Chi-square test for goodness of
fit, homogeneity of proportions,
and independence (one- and twoway tables)
III D Sampling distributions
8. Confidence interval for the slope
of a least-squares regression line.
“M&M Activity”
Chi-square and
Linear t test project
IV B Tests of significance
7. Test for the slope of a leastsquares regression line
1997 – 2006 AP Statistics Free
Response questions and available
multiple choice questions.
Supplemental AP practice resources,
APEX online review and practice
assessments, Student Conceptual
Outline (mentioned later).
Teaching Strategies and Philosophies
Non-calculus based discovery with the aid of technology
Advanced Placement Statistics is non-calculus based and seeks to provide students with a student-centered,
activity-based, learning environment where discovery and exploration of descriptive and inferential statistics
concepts drive intellectual experiences. The instructor serves as a facilitator and guide to learning. Students
are directed to explore aspects of the statistical process by forming hypotheses, designing procedures to test
those hypotheses using appropriate statistical techniques, analyzing problems and data, and drawing
conclusions.
It is important that all concepts and applications are rationalized by having students frequently reference realworld data and newspaper/online journal articles. Statistics should not only remain within the scope of the
educational environment, but be applied directly to students’ lives. Therefore, real data is used where
possible during the course, which translates into numbers with a context. An effort is made to revisit some
of the same data sets, examples and projects utilized in realizing descriptive statistical concepts, as students
grasp the inferential statistical concepts. The re-use of certain data sets and examples throughout the course
helps ease the transition from some of the more intuitive descriptive concepts to the more unfamiliar
inferential tests. For example, data is used from the random rectangle activity which explores different
methods of sampling, to determine good methods of sampling. The same data collected for each method of
sampling is used to create graphs (like dot-plots, box-plots, etc...) that students use to describe and compare
center, unusual features, shape and spread of the data. The data is also employed to introduce the bell-shape
and eventually extrapolate to the normal curve. Emphasis is placed on the importance of the normal
distribution (and binomial distribution) to the study of statistics, when data allows it. Students are trained to
carry out the process of simulation where appropriate in the course. Students utilize simulation and the
normal curve in discovering sampling distributions, and later on in performing inferential tests. They
concentrate on strategy and tools of basic data analysis before the instructor imparts inferential ideas to them.
This enables the learner to judge facts and figures presented to them in problems of scientific inference by
enlisting appropriate methods, conducting statistical analyses and developing inferences.
Success in this course and on the AP exam is, to a great extent, dependant on the students’ ability to
communicate statistics through writing. As a result, writing is an integral part of the course. Students are
taught how to write about data they gather and about concepts like sampling distributions, randomization,
random variables, etc…. They also learn how to write about statistical processes. Appropriate use of
statistical vocabulary is always stressed.
The instructor encourages students to focus on strategy and not just skill. For example, on inference
problems they must recognize the difference between samples, sampling distributions and populations. They
must be able to distinguish between sample and proportion. Students learn to verify the conditions required
for use of a statistical procedure before they carry it out. Emphasis is placed on the strategy of reading for
understanding. The learner discovers that all statistics problems come with context. Students utilize the
primary text, supplementary texts, the internet, journals, and actual AP exam questions to develop their
reading strategies and to discover statistics in context.
The abilities to learn, communicate, apply, connect and retain all aspects of the statistical process rely vastly
on an individual’s capacity to organize his/her lessons into notes, assignments, and reviews. Cumulative
review exercises and homework assignments are built into the course. This allows students to practice
selecting the best statistical method on the AP test when faced with problems based on any portion of the
course’s content. For review purposes, each student creates a Student AP Conceptual Outline as the course
advances. An excerpt of an example is shown towards the end of this document. The exam review process is
structured to maximize student performance. AP free response and multiple-choice questions from previous
AP exams are incorporated in all unit lessons and tests. They are also utilized, along with other exam
preparation resources, during the weeks of review leading up to the AP test.
Technology is an invaluable device when it comes to teaching and learning statistics. Since many of the
students are familiar with technology and some of its applications in their daily lives, the instructor builds off
their awareness when it comes to technology integration. Technology facilitates the process of learning to
work with data. Students use the TI graphing calculators and software like Minitab and Fathom so they can
focus their efforts on the development of concepts rather than on calculations. On the other hand, emphasis
is placed on the importance of accuracy and precision of calculations in drawing conclusions. Software
offers students experience using a representative statistical package and provides them with the opportunity
to read and analyze generic computer output. Students utilize applets in this course to run simulations and
discover underlying notions. The campus has purchased access for each AP student and teacher to
http://www.apexvs.com. This web-based resource provides flash animation lessons that include statistical
models and simulations. It also provides activities and online assessments that compliment the topics in the
AP Statistics Outline of Concepts. Students are provided with access to theses technologies that provide
empirical evidence of concepts, as well as provide effective dynamic demonstrations. Through the use of
calculators and computers, students enhance their development of statistical understanding by exploring and
analyzing data, assessing models, and performing simulations.
Assessment
Competency -Based Assessment
At the beginning of the course, each student is provided with a syllabus that includes an outline and timeline
of all AP Statistics course concepts, a summary of the types of course exams and projects, policies for
grading and rubric explanations, rationalization of reading and writing requirements, synopsis of technology
use, and information on the College Board and the Advanced Placement Test. Students are made aware of
the AP Central website early in the course and guided through a tour of its available resources that include
the AP Statistics Course Description and syllabus, AP Statistics exam tips for students, past AP Statistics
tests, sample responses, and scoring guides. Students are informed of the holistic grading scale that is used
throughout the course and on the AP test for scoring their free response answers.
Throughout the course, students are assessed in a variety of ways. Some are teacher-designed, activity-based
assessments that including simulations and interpretation of data. Assigned independent-study projects
require students to design, administer, collect data from, analyze, and write about surveys, experiments and
observational studies. Often students investigate data with the aid of software and then write a report that
describes the investigation and what was learned. Students are molded to draw on tools they have learned in
class to analyze information from statistically based articles. They follow through on their analysis by
writing a critical report on their findings. Students are assessed heavily on their ability to verify the
conditions required for use of a statistical procedure before they carry it out They are assessed acutely on
their ability to read, design, analyze and communicate methods, results and interpretations of the problem
being investigated, and use of proper statistical jargon. These skills are modeled and taught throughout the
course.
Tests are designed to be similar in form and difficulty level to the AP exam, consisting of multiple-choice
and free response questions, in order to prepare students for the format of the actual exam. Students are
permitted access to an AP Statistics test formula sheet on exams to prepare them to use this resource
efficiently when they take the exam.
These assessments emphasize:
 Written and oral communication of statistical concepts
 Connections between Design, Analysis and Interpretation in the context of the situation or application
 The use of technology to enhance the development of statistical understanding
 Group cooperation and collaboration
Student AP Conceptual Outline
This outline is not intended only as notes, but as a tool to help the students read, summarize and review
resources at the end of every topic. It serves as a review sheet, vocabulary definitions sheet, and statistics
manual which helps students gain a full command of the language of statistics, a skill essential to mastery
and AP test success.
The following is an excerpt from a student’s outline:
I. Exploring Data: Observing patterns and departures from patterns
Exploratory analysis of data makes use of graphical and numerical techniques to study
patterns and departures from patterns. Emphasis should be placed on interpreting
information from graphical and numerical displays and summaries.
A. Interpreting graphical displays of distributions of univariate data (dotplot, stemplot,
histogram, cumulative frequency plot)
1. Center and Spread – The center of a distribution is often called the median or the
middle of the data; it can also be called the mean which is an average of the data; the
spread of the distribution is called variance and it is how wide the data is distributed
about the center
2. Clusters and gaps – clusters in the distribution are places where there is some data
separated by gaps; one distribution could have many clusters; gaps in the distribution
are holes or places where there is a small amount of data in between the distribution
3. Outliers and other unusual features – individual observations that fall well outside
the overall pattern of the data
4. Shape – the overall pattern of the distribution for examples of shapes see I, C, 4
B. Summarizing distributions of univariate (one variable) data
1. Measuring center:
a. Median - to find median or the middle of the data:
Arrange all observations in order of size, from smallest to largest.
If the number n observations is odd, the median M is the center observation
in the ordered list. The location of the median is found by counting (n+1)/2
observations up from the bottom of the list.
If the number n observations is even, the median M is the average of the two
center observations in the ordered list.
b. Mean – If n observations are denoted by x1, x2, ..., xn their mean is:
x
1
x1  x 2  ...  x 3 
n
or in more compact notation:
x
1
 xi
n
Notes and Acknowledgements:
Even though the course outline above follows the chapters in the primary text (POD*), the text chapters are
supplemented with lessons, activities, problem sets, projects and data from other resources such as the
supplemental textbooks mentioned above, articles and journals, the College Board website, and other
technology resources. It is important to credit the authors of these textbooks, College Board writers and
presenters of the Advanced Placement Institutes for Statistics, for many of the resources implemented in this
course. They should also be credited for their expert insight into Advanced Placement and the subject of
Statistics, which has influenced the course design, teaching strategies and philosophies, and assessments.