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Course:
Grade Served:
Prerequisites:
Credit:
AP Statistics
11th & 12th grade
Algebra II, parent permission
2 credits
Course Description:
Students will continue developing an understanding of statistics through exploratory analysis, planning a study,
probability, and statistical inference. Students will explore and integrate statistical procedures through graphical
representations, observation of patterns, and formulation of models to make and test conjectures. This course is designed
to prepare students for the Advanced Placement Exam in May. A $5 calculator fee is required if the student chooses to
use the school calculators. Because students will not be allowed to use the school calculators outside of the classroom,
students will be strongly encouraged to purchase a TI-83 Plus graphing calculator that they will be required to use in this
and the remainder of their math courses. Students should see their most recent math teacher for a recommendation
Topics and/or Units Addressed:
1. Exploring Data: Observing Patterns and Departures from Patterns
A. Interpreting graphical displays of distributions of univariate data (dotplot, stemplot, histogram)
i) Center and Spread
ii) Clusters and Gaps
iii) Outliers and other unusual features
iv) Shape
B. Summarizing distributions of univariate data
i) Measuring center: median and mean
ii) Measuring spread: range, interquartile range and standard deviation
iii) Measuring position: quartiles, percentiles and standardized scores (z-scores)
iv) Using boxplots
v) The effect of changing units on summary measures
C. Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots)
i) Comparing center and spread: within group, between group variation
ii) Comparing clusters and gaps
iii) Comparing outliers and other unusual features
iv) Comparing shapes
D. Exploring bivariate data
i) Analyzing patterns in scatterplots
ii) Correlation and linearity
iii) Least Squares Regression line
iv) Residual plots, outliers and influential points
v) Transformations to achieve linearity: logarithmic and power transformations
E. Exploring categorical data: frequency tables
i) Marginal and joint frequencies for two-way tables
ii) Conditional relative frequencies and association
2. Planning a Study: Deciding what and how to measure
A. Overview of methods of data collection
i) Census
ii) Sample Survey
iii) Experiment
iv) Observational Study
B. Planning and conducting surveys
i) Simple random sampling
ii) Characteristics of a well designed and conducted survey
iii) Sampling error: the variation inherent in a survey
iv) Sources of bias in surveys
v) Stratifying to reduce variation
C. Planning and conducting experiments
i) Experiments versus observational studies versus surveys
ii) Confounding, control groups, placebo effects, blinding
iii) Treatments, experimental units, and randomization
iv) Completely randomized design for two treatments
v) Randomized paired comparison design
vi) Replication, blocking and generalizability of results
3. Anticipating Patterns: Producing Models using Probability and Simulation
A. Probability as relative frequency
i) “Law of Large Numbers”
ii) Addition Rule, Multiplication Rule, Conditional Probabilities, Independence
iii) Discrete random variables and their probability distributions
iv) Simulation of probability distributions, including binomial and geometric
v) Mean (expected value) and standard deviation of a random variable, including binomial
B. Combining Independent Random Variables
i) Notion of independence versus dependence
ii) Mean and standard deviation for sums and differences of independent random variables
C. The normal distribution
i) Properties of the normal distribution
ii) Using tables of the normal distribution
iii) The normal distribution as a model for measurements
D. Simulating Sample Distributions
i) Sampling distribution of a sample proportion
ii) Sampling distribution of a sample mean
iii) Central Limit Theorem
iv) Sampling distribution of a difference between two independent sample proportions
v) Sampling distribution of a difference between two independent sample means
4. Statistical Inference: Confirming Models
A. Confidence Intervals
i) The meaning of a confidence interval
ii) Large sample confidence interval for a proportion
iii) Large sample confidence interval for a mean
iv) Large sample confidence interval for the difference between two proportions
v) Large sample confidence interval for the difference between two mean (unpaired and paired)
B. Tests of Significance
i) Logic of significance testing, null and alternative hypotheses; p-values; one and two sided tests
ii) Large sample test for a proportion
iii) Large sample test for a mean
iv) Large sample test for a difference between two proportions
v) Large sample test for a difference between two means (unpaired and paired)
vi) Chi-Square test for goodness of fit, homogeneity of proportions, and independence
C. Special case of normally distributed data
i) t-distribution
ii) Single sample t procedures
iii) Two sample (independent and matched pairs) t procedures
iv) Inference for slope of least squares line
Resources/Web Link to Textbook:
Academic Expectations:
2.7
2.8
2.9
2.10
2.11
2.12
2.13
Students understand number concepts and use numbers appropriately and accurately.
Students understand various mathematical procedures and use them appropriately and accurately.
Students understand space and dimensionality concepts and use them appropriately and accurately.
Students understand measurement concepts and use measurements appropriately and accurately..
Students understand mathematical change concepts and use them appropriately and accurately.
Students understand mathematical structure concepts including the properties and logic of various mathematical
systems.
Students understand and appropriately use statistics and probability.
Standards/Core Content/Program of Studies Addressed:
POWER STANDARD
MA-11-4.1.1
Assessed
Students will analyze and make inferences from a set of data with no more than two variables, and will analyze situations
for the use and misuse of data representations. (Linear ONLY)
DOK – 3
SUPPORTING CORE CONTENT
MA-11-4.1.2
Assessed
Students will construct data displays for data with no more than two variables.
DOK – 2
MA-11-4.2.1
Assessed
Students will describe and compare data distributions and make inferences from the data based on the shapes of graphs,
measures of center (mean, median, mode) and measures of spread (range). (focus on calculating mean, median, mode
and range)
DOK – 2
MA-11-4.3.1
Assessed
Students will recognize inappropriate strategies for data gathering (e.g., non-random sampling, polling only a specific
group of people, using limited or extremely small sample sizes, bias issues) and explain why these strategies can lead to
inaccurate inferences.
DOK – 2
MA-11-4.3.2
ADP Benchmark
Students will design simple experiments or investigations to collect data to answer questions of interest.
MA-11-4.3.3
ADP Benchmark
Students will explain the differences between randomized experiments and observational studies.