Course of Study

ADVANCED PLACEMENT STATISTICS

The purpose of the Advanced Placement course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data.  Students are exposed to four broad conceptual themes:

(1)	Exploring data:  Observing patterns and departures from patterns.
(2)	Planning a Study:  Deciding what and how to measure.
(3)	Anticipating patterns:  Producing models using probability theory and simulation
(4)	Statistical Inference:  Confirming models.

Intended audience:

The AP Statistics course may be taken by any student who has successfully completed a second year course in Algebra (or equivalent) and will be useful for any college-intending student regardless of the students intended college major.

This course addresses the following district student learning outcomes:

#1  Communicate articulately, effectively, and persuasively, when speaking and writing.
#2  Read and analyze material in a variety of disciplines.
#3  Use technology as a tool to access information, analyze and solve problems, and               communicate ideas.
#4  Apply mathematics knowledge and skills to analyze and solve problems.

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.

To complete the AP Statistics course, students will:

A.  Interpret graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot) including:
	1.  Center and spread
	2.  Clusters and gaps
	3.  Outliers and other unusual features
	4.  Shape

B.  Summarize distributions of univariate data, including:
	1.  Measuring center:  median, mean
	2.  Measuring spread:  range, interquartile range, standard deviation
	3.  Measuring position:  quartiles, percentiles, standardized scores (z-scores)
	4.  Using boxplots
	5.  Analyzing the effect of changing units on summary measures

C.  Compare distributions of univariate data (dotplots, back-to-back stemplots, parallel boxlots) including:
	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

D.  Explore bivariate data including:
	1.  Analyzing patterns in scatterplots
	2.  Correlation and linearity
	3.  Least-squares regression line
	4.  Residual plots, outliers, and influential points
	5.  Transformations to achieve linearity:  logarithmic and power transformations

E.  Explore categorical data:  frequency tables including:
	1.  Marginal and joint frequencies for two-way tables
	2.  Conditional relative frequencies and association

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.

To complete the AP Statistics course, students will:

A.  Describe the overview of methods of data collection, including:
	1.  Census
	2.  Sample survey
	3.  Experiment
	4.  Observational study

B.  Plan and conduct surveys using:
	1.  Characteristics of a well-designed and well-conducted survey
	2.  Populations, samples, and random selection
	3.  Sources of bias in surveys
	4.  Simple random sampling
	5.  Stratified random sampling

C.  Plan and conduct experiments using:
	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

D.  Determine generalizability of results from observational studies, experimental studies, and surveys

Probability is the tool used for anticipating what the distribution of data should look like under a given model

To complete the AP Statistics course, students will investigate the following probability concepts and statistical models using probability and simulation:

A.  Use of probability as relative frequency including:
	1.  “Law of large numbers” concept
	2.  Addition rule, multiplication rule, conditional probability, and independence
	3.  Discrete random variables and their probability distributions, including                   binomial
	4.  Simulation of probability distributions, including binomial and geometric
	5.  Mean (expected value) and standard deviation of a random variable, and linear                   transformation of a random variable

B.  Combinations independent random variables including:
	1.  Notion of independence versus dependence
	2.  Mean and standard deviation for sums and differences of independent random                   variables

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

D.  Sampling distributions including:
	1.  Sampling distribution of a sample proportion
	2.  Sampling distribution of a sample mean
	3.  Central Limit Theorem
	4.  Sampling distribution of a difference between two independent sample                   proportions
	5.  Sampling distributions of a difference between two independent sample means
	6.  Simulation of sampling distributions

To complete the AP Statistics course students will work problems and undertake projects which include the following statistical ideas:

A.  Confidence intervals
	1.  The meaning of a confidence interval
	2.  Large sample confidence interval for a proportion
	3.  Large sample confidence interval for a mean
	4.  Large sample confidence interval for a difference between two proportions
	5.  Large sample confidence interval for a difference between two means                   (unpaired and paired)

B.  Tests of significance
	1.  Logic of significance testing, null and alternative hypotheses, p-values; one-                   and two-sided tests; concepts of Type I and Type II errors; concept of power
	2.  Large sample test for a proportion
	3.  Large sample test for a mean
	4.  Large sample test for a difference between two proportions
	5.  Large sample test for a difference between two means (unpaired and paired)
	6.  Chi-square test for  a goodness of fit, homogeneity of proportions, and                    independence (one- and two-way tables) 

C.  Special case of normally distributed data
	1.  t-distribution
	2.  Single sample t procedures
	3.  Two sample (independent and matched pairs) t procedures

4.	Inference for the slope of least-squares regression line

A.  Student Assessment

Ultimately students will be assessed by their scores on the AP Statistics Examination.  During the year students will be assessed by their performance on quizzes, examinations, and projects.  Criteria for grading and course expectations will be given to students at the beginning of the course, preferably in writing.

B.  Course Assessment

The success of the course will be judged by the scores of students on the AP Statistics Exam and by student survey.

Students will use manipulatives, writing, group exploration, discussion, homework, presentations, and projects including surveys and experiments.  Teachers are available for out-of-class assistance; the process will be established for each class and made known to students at the beginning of the semester.

The course will be based on an appropriate AP Statistics textbook (see approved textbook list) and the capabilities of an AP Statistics approved graphing calculator.  Students will use Ti-83 (or equivalent) calculators daily in class.

A.  Prerequisites

Students must complete Advanced Algebra or equivalent with a grade of B or better; or students must complete Precalculus or equivalent with a grade of C or better.

B.  Requirements Met

AP Statistics satisfies one year (10 credits) of the district’s mathematics graduation requirement or may be used for elective credit.  AP Statistics is accepted for the University of California’s “g” requirement.

Approved: 2/25/97
Revised:    5/31/02