Curriculum Documents by Quarter - Mathematics AP Statistics

Learning Objectives

Students should understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each

Students should know the characteristics of well-designed studies, including the role of randomization in surveys and experiments

Students should understand histograms, parallel box plots, and scatterplots and use them to display data

Students should be able to display the distribution, describe its shape, and select and calculate summary statistics

Students should understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference

Students should be able to evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions

• What are different ways of representing, organizing, and relating numbers to mathematical operations?
• How do we understand and represent patterns, relationships, and change?
• What are the characteristics, properties, and applications of multi-dimensional shapes? 
• How do we collect, organize, display, and analyze data? 
• Which strategies and mathematical operations are used to solve problems and arguments, and how can we develop and improve them?
• How can mathematical thinking be effectively communicated to different audiences? 
• How are mathematical concepts related to one another, other disciplines, and to the real world?

 Vocabulary

Learning Objectives

To understand the four methods of data collection (census, sample survey, experiment, observational study).

To understand the characteristics of a well-designed and well-conducted survey.

To understand different sampling methods, including but not limited to simple random samples, stratified random samples, and cluster samples.

To describe characteristics of a well-designed and well conducted experiment, taking into account biases such as the placebo affect.

To construct and interpret graphical displays of distributions of univariate data using methods such as the dot plot, stem and leaf, histogram, and cumulative frequency plot.

To summarize distributions of univariate data…by measuring center, spread, and position.

 Students should, for univariate
measurement data, be able to
display the distribution, describe its shape, and select and calculate summary statistics

Students should be able to
evaluate published reports that
are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions

Students should understand the concepts of sample space and probability distribution and
construct sample spaces and
distributions in simple cases

Students should be able to use
simulations to construct
empirical probability
distributions

Students should be able to
compute and interpret the
expected value of random
variables in simple cases

Students should understand the concepts of conditional
probability and independent
events

Students should understand how to compute the probability of a compound event

• What are different ways of representing, organizing, and relating numbers to mathematical operations?
• How do we understand and represent patterns, relationships, and change?
• What are the characteristics, properties, and applications of multi-dimensional shapes? 
• How do we collect, organize, display, and analyze data? 
• Which strategies and mathematical operations are used to solve problems and arguments, and how can we develop and improve them?
• How can mathematical thinking be effectively communicated to different audiences? 
• How are mathematical concepts related to one another, other disciplines, and to the real world?

 Vocabulary

 Students should understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable

Students should compute basic
statistics and understand the
distinction between a statistic and a parameter

Students should, for univariate
measurement data, be able to
display the distribution, describe its shape, and select and calculate summary statistics

Students should, for bivariate
measurement data, be able to
display a scatterplot, describe its shape, and determine regression coefficients, regression equations,
and correlation coefficients using technological tools

Students should display and
discuss bivariate data where at
least one variable is categorical Students should identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled

Students should understand how sample statistics reflect the values of population parameters and use
sampling distributions as the basis for informal inference

• What are different ways of representing, organizing, and relating numbers to mathematical operations?
• How do we understand and represent patterns, relationships, and change?
• What are the characteristics, properties, and applications of multi-dimensional shapes? 
• How do we collect, organize, display, and analyze data? 
• Which strategies and mathematical operations are used to solve problems and arguments, and how can we develop and improve them?
• How can mathematical thinking be effectively communicated to different audiences? 
• How are mathematical concepts related to one another, other disciplines, and to the real world?

Vocabulary

Learning Objectives

Properties of the normal distribution Using tables of the normal
distribution 

The normal distribution as a modelfor measurements

The Central Limit Theorem Properties of point estimators,
including unbiasedness and variability

 Students should compute basic statistics and understand the distinction between a statistic and a parameter.

Students should use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions.

Students should understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference.

Students should evaluate
published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions.

• What are different ways of representing, organizing, and relating numbers to mathematical operations?
• How do we understand and represent patterns, relationships, and change?
• What are the characteristics, properties, and applications of multi-dimensional shapes? 
• How do we collect, organize, display, and analyze data? 
• Which strategies and mathematical operations are used to solve problems and arguments, and how can we develop and improve them?
• How can mathematical thinking be effectively communicated to different audiences? 
• How are mathematical concepts related to one another, other disciplines, and to the real world?

 Vocabulary

Learning Objectives

Logic of confidence intervals, meaning of confidence level and
confidence intervals, and properties of confidence intervals

Confidence interval for a mean, and large sample confidence interval for a proportion

Confidence interval for a difference between two means (unpaired and paired) t-distribution and Chi-square
distribution

Logic of significance testing, null and alternative hypotheses, p-values, one and two sided tests, concepts of Type I and Type II errors

Large sample test for a proportion

Sampling distribution of a difference between two independent sample means

Sampling distribution of a difference between two independent sample proportions