AP Statistics
AP Statistics is a year-long every other day (A-day/B-day) class. Each period is
90 minutes. Students enrolled in the course passed an Honors level Algebra II course, a
Pre-Calculus course, or both. The majority of the students are 11th and 12th graders, some
taking Pre-Calculus or AP Calculus concurrently. Select 10th grade students are also
permitted to take the course but are rare, 1 or 2 a year. For many students this is the first
and sometimes only AP course they take. Students must take the AP Statistics Exam in
May.
COURSE CONTENT
The Course is based on the objectives listed in the topic outline for AP Statistics from the
College Board. The TI-83 plus graphing calculators are used on a daily by the students
and used by the instructor to model their used in this course. TI-89 calculators are used
by some students. Explanation of this calculator’s uses for statistical calculations is
explained in detail in the textbook used. Student used built-in statistical functions of the
TI-83 plus, such a 1-varstats, normcdf, etc. Additionally, the TI-83 plus calculator
applications, including catalog help and the probability simulator, are also used. Students
are asked to discover the connection between calculator graphical displays, tabular
displays and results from calculator functions and the concept of the day. Examples of
topics where this approach is used are: finding an outlier, determining symmetry or
skewness from boxplots, etc. The instructor models the use of each of the calculator
processes on an overhead calculator display.
Computer resources are also used by the instructor to promote the understanding and
interpretation of computer printouts which is essential to success on the AP Exam.
Students are introduced to Minitab through the course and encouraged to use Excel when
preparing and writing the statistical project that is required in this course.
The project is due at the end of March. From experience this has proven to provide
enlightenment for how everything works together for students who have not yet seen the
connections. The project shows students how planning and conducting a study,
describing patterns and departures from those patterns, using concepts involving random
phenomena to understand the integration of collected data and the pattern seen and
making inferences based on the entire process and an appropriate statistical test all fits
together.
Students are assigned approximately 60 minutes of homework per class. Tests are
administered about every two weeks as units are completed. Supplementary materials
and laboratory activities are used in each unit to supplement the text. A four week review
for the AP Exam is built into the pacing guide. Students regularly work in group settings
when conducting laboratory activities and solving problems in class.
Each unit test is made up using Free Response questions from prior exams, these are also
used during the review. In the process of solving Free Response questions students
practice writing explanations. These explanations are based on the appropriate
interpretations/processes used to draw conclusions from the calculated values. Students
are expected to learn the mechanics of writing statistical interpretations and are instructed
from the beginning of the course to use writing techniques.
Students will take a full length practice exam prior to the May test date. A released Exam
will be used for this purpose.
COURSE OUTLINE & PACING GUIDE
TOPIC 1:
EXPLORING DATA
(6 days- Goals 1 through 3, however this material is reviewed and applied repeatedly
throughout the course.)
Goal 1:
The leaner will construct and interpret graphical displays of univariate data.]
Objectives:
Goal 2:
The learner will apply numerical measurements to summarize distributions.
Objectives:
Goal 3:
Construct plots from the data, including dotplot, stemplot,
histogram, cumulative frequency plot with and without
the TI-83 plus (including the used the Stat Editor and
StatPlot functions). Find center and spread, clusters,
gaps, probable outliers, and shape from graph. Determine
best graph to used based on shape of distribution.
Calculate center (median and mean), spread (range,
interquartile range and standard deviation), and position
(quartiles, percentiles, standardized scores) with and
without the TI-83 plus (including 1-var stat function and
boxplot.)
Collect biased data by convenience sampling to apply
summary concepts and make conjectures.
Examine the effect of changing units of measure on
summary measures.
Determine best measures to be used based on shape of
distribution.
Write analysis of summary statistics using shape, center
and spread, and deviations.
The leaner will compare distributions of univariate data pictured graphically.
Objectives:
Write comparative statements about sets of data from
both within the set and between multiple sets using
information garnered from Goal 2, (shape, center and
spread, and deviations).
Determine best measures to use for distributions
based on shaped and spread of distributions,
especially the middle 50% of the data.
(8 days- Goal 4)
Goal 4:
The learner will explore bivariate data.
Objectives:
Analyze graphical displays of bivariate data,
discussing form, direction, strength and deviations.
Analyze data numerically for determination of form,
direction, strength and deviations (correlation.)
Calculate the equation of the linear sets of data.
Determine linearity using graphical displays and
numerical calculations (residual plots, residual values,
correlation, outliers and influential points.).
Use linear concepts to transform logarithmic and
power functions and to verify the type of graph
formed.
Collect biased data from convenience
samples to practice interpretation of bivariate data,
examine computerized graphical displays and outputs
and write descriptions of data using appropriate
vocabulary, calculations and analysis. Use the TI-83
plus to calculate descriptive numerical calculations
for bivariate data and to create graphs of this data.
(2 days- Goal 5, however this material will be used throughout the course and will be
applied accordingly.)
Goal 5:
The learner will explore categorical data.
Objectives:
Construct frequency tables and bar graphs.
Construct two-way tables and segmented bar
graphs.
Calculate marginal and joint frequencies from this
Data using the information garnered to interpret
meaning of statistical data in contextual situations.
Compare distributions using both bar charts and
Segmented bar graphs and write an appropriate
analysis of the information.
TOPIC 2:
SAMPLING AND EXPERIMENTATION
(7 days- Goals 6 through 9)
Goal 6:
The learner will examine methods of data collection.
Objectives:
Goal 7:
The learner will study concepts needed to plan and conduct survey.
Objectives:
Goal 8:
Determine the typed of collection method used to gather
data; census, variety of types of sampling, variety of types
experiments and observational studies.
Learn the characteristics of a well-designed and wellconducted survey, including but no limited to the wording
of questions and the appearance interviewer.
Determine the population to be studied, the method to be
used to randomly select a sample, and possible sources of
bias.
Identify the type of sampling method to be used for best
results in a survey: simple random sampling, stratified
random sampling, and cluster sampling.
Randomly select a sample from a defined population (this
is part of the project to be conducted at the end of the year).
Write a description of the process followed to correctly
design a survey, including but not limited to the process
used to acquire a random sample.
The learner will study concepts needed to plan and conduct experiments.
Objectives:
Learn the characteristics of a well-designed and wellconducted experiment, including treatments, control
groups, experimental units, random assignment and
replication.
Conduct a group experiment where all aspects of a welldesigned experiment are discussed and incorporated into
the activity and then carried out.
Determine sources of bias and/or confounding that may
cause results of the experiment to be unreliable, including
used of placebos and blind and double-blind methods.
Design experiments using the methods of complete
randomization, randomized block design and matched pairs
designs.
Write a description of the complete process used in
designing an experiment.
Goal 9:
The learner will apply generalize the results and types of conclusions that
can be drawn from observational studies, experiments, and surveys and be
able to explain this generalization in written form.
TOPIC 3:
ANTICIPATING PATTERNS
(35 days-Goals 10 through 13)
Goal 10:
The learner will explore random phenomena using probability.
Objectives: Interpret probability, including long-run relative frequency
interpretation.
Analyze expected outcomes using the “Law of Large Numbers”.
Perform probability calculations using addition and multiplication
rules, conditional probability and rules for independence.
Calculate probabilities for discrete random variables and their
probability distributions, including binomial and geometric
distributions.
Stimulate data based on random behavior and probability
distributions, including the use of the TI-83 plus application ProbSim.
Calculating expected value and standard deviation of a random
variable, including by TI-83, plus functions, and transforming random
variables linearly.
Goal 11:
The learner will calculate probabilities for independent random variables.
Objectives: Determine the independence of a random variable distribution.
Calculate mean and standard deviation for sums and differences of
independent random variables.
Goal 12:
The learner will apply the probability of the normal distribution.
Objectives: Learn the properties of the normal distribution.
Use tables and TI-83 plus calculator functions, normcdf and invnorm,
to find probability values for normal distributions.
Use the normal distribution as a measure to describe data.
Goal 13:
The learner will apply the probability of sampling distributions.
Objectives: Apply the concept of sampling distributions to calculate probabilities
involving a sample proportion, the difference between two
independent sample proportions, a sample mean and the difference
between two sample means.
Apply the Central Limit Theorem.
Use simulation techniques and the TI-83 plus calculator to simulate
sampling distributions.
Apply probability calculations to both distributions and Chi-square
distributions.
TOPIC 4:
STATISTICAL INFERENCE
(28 days- Goals 14 &15)
Goal 14:
The learner will use statistical inference to estimate confidence intervals.
Objectives: Estimate population parameters and margins of error.
Use properties of point estimators, including bias and variability.
Analyze confidence intervals explaining the meaning of the
confidence level and interval.
Calculate large sample confidence intervals for a proportion and the
difference between two proportions, both with and without the TI-83
plus confidence interval functions.
Calculate confidence intervals for a mean and the difference between
two means, both with and without the TI-83 plus confidence interval
functions.
Calculate confidence intervals for the slope of a least-squared
regression line, both with and without the TI-83 plus confidence
interval functions.
Analyze the results of a confidence interval and put the analysis in
written form.
Goal 15:
The learner will use statistical inference with tests of hypothesis.
Objectives: Apply the logic of significance tests with regard to hypotheses, pvalues, and one- and two- sided tests.
Determine the Type I and Type II errors involved in specific
application problems.
Determine the accuracy of results based on the concept of power.
Calculate the results of significance testing for large sample
proportions and the difference between two proportions, for a mean
and the difference between two means, Chi-square goodness of fit,
homogeneity of proportions, and independence for one- and two-way
tables, and the slope of a least-squares regression line, both with and
without the TI-83 plus calculator functions.
Analyze the results of significance tests and put the analysis in written
form.
(20 days)
Goal 16:
The learner will review all materials taught in this course in preparation
for the AP Exam.
(15 days)
Goal 17:
The learner will present results of statistical to project to members of the
AP class and will explore the use of statistics in careers.
The balance of the days will be used for Formal Mid-term and Term Examinations.
References and Materials
Primary Textbook:
Yates, Daniel S., Moore, David S., and Starnes, Daren S. The Practice of Statistics.
2nd ed. New York: W.H. Freeman and Company, 2003. ISBN: 0-7167-4773-1.
References:
Yates, Daniel S., and Starnes, Daren S. Golden Resource Binder. New York: W.H.
Freeman and Company, 2002. ISBN: 0-7167-8345-2.
Statistics: Decisions Through Data. COMAP, Lexington, MA 1-800-772-6627.
www.comap.com
Scheaffer, Richard, et al., Activity Based Statistics: Instructor Resources. New York:
SpringerVerlag, 1996. ISBN 0-387-94597-0.
Technology:
TI-83 plus and TI-89 graphing calculators
Minitab statistical software.
Microsoft Excel software.