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AP Statistics Syllabus
Paul Buckley
Gonzaga College High School
Washington D.C.
School Profile
School Environment: Gonzaga College High School is a private college preparatory
school for boys with approximately 930 students in grades 9-12. Nearly all graduates go
on to a four-year college. Approximately 20 percent of our students complete Advanced
Placement Statistics.
All math classes meet every day for at least 40 minutes. Approximately one out of every
eight days, each class meets for 70 minutes. Our school year consists of about 170 days,
of which about 140 are class days before the AP® Exams.
Course Sequences Leading to Statistics:
Students eligible to take Statistics will qualify under one of the following criteria:
 Having passed AP Calculus AB
 Having passed AP Calculus BC
 Having passed Honors Precalculus with a C+ or better average
 Having passed Precalculus with a B- or better average
 Having passed Honors Algebra II & Trig with an A- or better average
 Having passed Algebra II & Trig with an A average & excellent work habits
 Having passed AP Algebra II & Intro Calculus
Course Content:
Throughout the year, students will be exposed to four broad conceptual themes,
Exploring Data, Planning A Study, Anticipating Patterns, and Statistical Inference.
While the pure mathematics involved is not complicated, this course does require a
“mathematical maturity” and interpretive and reasoning skills which the students may not
have fostered as much in previous math courses. Written work and the ability to express
one’s mastery of a problem through words is a major component of this course.
Further clarification of written work:
Many of the questions in AP Statistics deal with interpreting data, often in a written form.
Toward this end, there are written assignments throughout each quarter. These
assignments are in paragraph form, using proper grammar and spelling, and should be
indicative of students capable of higher-level thinking. The assignments are designed to
make the real-life connection between the math that is used and the context in which it is
used. It is not enough in this case to just get a proper answer. The methodology behind
the answer and the understanding of where that answer fits in the greater context of the
problem is preeminent in this course.
Bibliography:
Bock, David E., Paul F. Velleman, and Richard D. DeVeaux. Stats: Modeling the World.
Boston: Pearson/Addison-Wesley, 2004
Yates, Daniel S., David S. Moore, and Daren S. Starnes. The Practice of Statistics. New
York: W.H. Freeman, 2003.
Scheaffer, Richard, Mrudulla Gnanadesikan, Ann Watkins, and Jeffrey A. Witmer,
Activity-Based Statistics. New York: Springer-Verlag 1996.
Carrol, Carver, Peters and Ricks, Preparing for the Statistics AP Exam with Stats:
Modeling the World, Boston: Pearson/Addison-Wesley, 2004
Millard, Ron, and John C. Turner, Activities and Projects for High School Statistics
Courses. New York: W.H. Freeman, 2004
Orkin, Mike, What are the Odds? Chance in Everyday Life. New York: W.H. Freeman,
2000
Huff, Darrell, How to Lie With Statistics, New York: W. W. Norton & Co. 1982
Technology:
All students are required to bring their own graphing calculator to class every day.
Almost all students have the TI-83+ or TI-89 Graphing Calculator. Those that have a TI89 that do not have the Stats/List Editor have it downloaded onto their calculator so that
they all have the same software available.
The teacher’s computers as well as the math computer lab across the hall all have Excel
and Minitab on their computers for labs that necessitate a statistical software package.
The classroom computer is also hooked up to an LCD monitor so that web applets may
be showed to the whole class.
In the course of the year, students use Technology in the following scenarios:
Unit 1
 Entering a list of data on a calculator
 Creating and interpreting a bar or pie chart through a spreadsheet program
 Creating and interpreting a boxplot, dotplot or histogram
 Calculating the five-number summary for a set of data
 Calculating the mean and standard deviation for a set of data
 Checking for outliers in a set of data
 Finding Normal Percentiles from the Standard Normal Distribution
 Finding a z-score from a Percentile
 Creating a Normal Probability Plot
Unit 2
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Creating and interpreting a scatterplot
Calculating and interpreting the correlation coefficient
Calculating and interpreting the coefficient of determination
Calculating the least squares regression line for bivariate data
Creating a residual plot
Creating a regression line from Statistical Software output
Looking at the effect of outliers and influential points on a scatterplot and
its correlation through web applets.
Re-expressing data through non-linear regression
Unit 3
 Running a simulation
 Creating a random sample through a random number generator
Unit 4
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Calculating basic probabilities
Calculating the mean and standard deviation of a random variable
Running a Geometric Probability Model
Running a Binomial Probability Model
Unit 5
 Verifying the Central Limit Theorem
 Creating a Confidence Interval for Proportions
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Conducting a One-Proportion z-test
Creating a Confidence Interval for Two Proportions
Conducting a Two-Proportion z-test
Unit 6
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Creating a One-sample t-interval
Conducting a One-sample t-test for the mean
Creating a Two-sample t-interval
Conducting a Two-sample t-test for the mean
Conducting a Matched Pairs t-test
Unit 7
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Conducting a Chi-Square Goodness-of-Fit test
Conducting a Chi-Square test for Homogeneity or Independence
Conducting a Regression Slope t-test
Interpreting a Regression Slope t-test through statistical software output
Course Outline
Chapter 1: Stats Starts Here (time: 1 day)
 Activity: Opening Day Survey
Unit 1: Exploring and Understanding Data (time: 5 weeks)
 Categorical vs Quantitative data
 Displaying and Describing Categorical Data
o Relative frequency table
o Bar charts
o Pie charts
o Contingency tables – marginal & conditional distributions
o Independence
o Segmented bar chart
o Simpson’s Paradox
 Displaying Quantitative Data
o Histograms
o Stem-and-Leaf Display
o Dotplot
o Center, Shape and Spread
o Modes – unimodal, bimodal, uniform
o Symmetry, skewness
o Outliers
o Timeplot
o Cumulative frequency graphs
 Activity: Matching Graphs to Variables
 Describing Distributions Numerically
o Center - Mean, median, midrange
o Spread – range, interquartile range, percentiles
o 5-number summary
o Boxplots
o Variance & Standard deviation
 Activity: Matching Statistics to Graphs
 Standard Deviation and the Normal Model
o Standardized values – z-scores
o Standard Normal distribution
o Empirical rule (68-95-99.7 rule)
o Normal probability plot
Unit 2: Exploring Relationships Between Variables (time: 4 weeks)
 Scatterplots, Association and Correlation
o Scatterplot
o Association - Direction and strength
o Explanatory and response variable
o Correlation – strength of a linear relationship
o R – correlation coefficient
o Correlation vs Causation
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Activity: Matching Correlations to Scatterplots (web applet)
Linear Regression
o Linear model
o Residual
o Least squares regression line
o Coefficient of determination – r2
o Residual plot – what to look for
o Extrapolation
o Outliers – influential points
o Lurking variables
Re-expressing Data
Unit 3: Gathering Data (time: 3 weeks)
 Understanding randomness
o Simulation
o Table of random digits
 Activity: Yahtzee
 Sample Surveys
o Population, sample
o Bias, randomization
o Sample size, census
o Population parameter vs sample statistic
o Simple random sample (SRS)
o Sampling frame, sampling variability
o Stratified random sample, cluster, multistage, systematic
o Convenience, voluntary response sample
o Undercoverage, nonresponse, response bias, wording of questions
 Experiments
o Observational study
o Response, subjects, experimental units, treatments, factors, levels
o Principles of Experimental Design: Control, Randomness,
Replication
o Blocking
o Statistically Significant
o Control group, single- and double-blind, placebo
o Matched Pairs
o Lurking variables, confounding variables
Unit 4: Randomness and Probability (time: 4 weeks)
 From Randomness to Probability
o Probability, trial, outcome, event
o Independence, mutually exclusive (disjoint)
o Law of Large Numbers
o Addition Rule and Multiplication Rule
 Probability Rules
o Sample space
o Conditional probability
o Tree diagrams
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Random Variables
o Random variables: discrete and continuous
o Probability model
o Expected value (mean) and standard deviation
o Sum and difference rules for mean and variance
Activity: Playing the lottery
Probability Models
o Bernoulli trials
o Geometric probability model
o Binomial model
o Binomial setting
o Normal model
o 10% condition, success/failure condition
Unit 5: From the Data at Hand to the World At Large (Statistical Inference Pt 1) (time:
5 weeks)
 Sampling Distribution Models
o Sampling Distribution Model for a Proportion
o Approximation to Normal Models
o Assumptions and Conditions
o Sampling Distribution Model for Means
o Central Limit Theorem
o Importance of Random Sampling and Independence
o Affect of Sample Size on Standard Deviation
o Standard Deviation vs Standard Error
 Activity: Cents and the Central Limit Theorem
 Activity: Random Rectangles
 Confidence Intervals for Proportions
o Margin of Error: Certainty vs Precision
o Critical Values
o Assumptions and Conditions
o One-proportion z-interval
o Interpretation of Interval in context
o Interpretation of Confidence level in context
 Activity: Estimating Proportions: How Accurate Are the Polls?
 Testing Hypothesis about Proportions
o Null and Alternative Hypothesis
o Retain and Rejecting the Null
o The Logic/Reasoning of a Hypothesis Test
o Calculating the Test statistic and P-value
o One-proportion z-test
o Conclusion – always in context
o One-sided vs two-sided alternative
o How to interpret a P-value
o Using a confidence interval as a follow-up to a Hypothesis Test
o P-Value vs Alpha Level – when is it statistically significant?
o Type I and Type II errors
o Power of a test
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o How to reduce Type I and Type II errors – effect of sample size
Comparing Two Proportions
o Variance of the sum or difference of two independent random
variables
o Standard Deviation of the Difference Between two proportions
o Assumptions and Conditions
o Sampling Distribution Model for difference between two
proportions
o Two-Proportion z-interval
o Pooling the data
o Two-Proportion z-test
Unit 6: Learning About the World (Statistical Inference Pt 2) (time: 4 weeks)
 Inferences About Means
o When can’t you use a z-distribution?
o T-distributions
o Degrees of freedom
o Sampling Distributions for means
o Assumptions and Conditions – Nearly Normal
o One-sample t-interval
o One-sample t-test for the mean
o Significance vs importance
o Sample Size – how large is enough?
 Comparing Means
o Comparing data through side-by-side graphs
o Comparing two means
o Z or t?
o Two-sample t-interval for means
o Two-sample t-test for means
o Sampling Distribution for the difference between two means
o Calculating the degrees of freedom
o Pooled t-test
 Paired Samples and Blocks
o When can data be paired?
o Matched Pairs t-test
o Paired Data Assumption
o Matched Pairs t-interval
o Blocking
Unit 7: Inference When Variables are Related (time: 2 weeks)
 Chi-Square Distributions
o Goodness-of-fit test
o Assumptions and Conditions – counted data, expected cell
o Calculating a Chi-Square statistic
o Chi-Square test for Homogeneity
o Chi-Square test for Independence
o Contingency tables
o Examining the residuals
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Inferences for Regression
o Variability in the regression line
o Assumptions and Conditions
o Standard Error for the slope
o Sampling Distribution for regression slopes
o Regression Slope t-test
o Confidence Interval for slope
Review for AP Exam: (time: 3 weeks)
Post AP-Exam: End of the year Project: (time: 2 weeks)