 White Plains Public Schools
 Curricula

AP Statistics: This Advanced Placement course provides the opportunity for students who have a strong desire to study an advanced mathematics course on the Advanced Placement level. Topics such as exploring data and observing patterns and departures from patterns, planning a study, producing models using probability theory and simulation, and statistical inference are included in the course. *The students are required to pay the fee and take the Statistics Advanced Placement Exam in order to receive the weighted final grade. The final exam is a departmental exam.
Please note that the timelines listed below are a guide. Teachers modify their pacing based on student needs in order to ensure concept mastery.Unit 1
Exploring Data
September
Section
Concept
Objectives
Textbook Resources
Intro
Data Analysis
Identify the individuals and variables in a set of data.
Pages 27
Intro
Classify variables as categorical or quantitative.
Pages 27
1.1
Bar Graphs and Pie Charts
Identify units of measurement for a quantitative variable.
Pages 810
1.1
Make a bar graph of the distribution of a categorical variable
Pages 810
1.1
Recognize when a pie chart can and cannot be used.
Pages 810
1.1
Identify what makes some graphs deceptive.
Pages 1112
1.1
TwoWay Tables
From a twoway table of counts, answer questions involving marginal and conditional distributions.
Pages 1214
1.1
Describe the relationship between two categorical variables
Pages 1415
1.1
Construct bar graphs to display the relationship between two categorical variables.
Pages 1619
1.2
Comparing Distributions
Make a dotplot or stemplot to display small sets of data.
Pages 2728
1.2
Describe the overall pattern (shape, center, spread) of a distribution
Pages 2932
1.2
Identify the shape of a distribution from a dotplot, stemplot, or histogram as roughly symmetric or skewed.
Pages 2932
1.2
Histograms
Make a histogram with a reasonable choice of classes.
Pages 3541
1.2
Interpret histograms.
Pages 3537
1.3
Measuring Centers Identifying Outliers
Calculate and interpret measures of center (mean, median) in context
Pages 5055
1.3
Calculate and interpret measures of spread (IQR) in context
Pages 5557
1.3
Identify outliers using the 1.5 × IQR rule.
Pages 5759
1.3
Five Number Summary and Standard Deviation
Make a boxplot.
Pages 5961
1.3
Calculate and interpret measures of spread (standard deviation)
Pages 6266
1.3
Select appropriate measures of center and spread
Pages 6668
1.3
Use appropriate graphs and numerical summaries to compare distributions of quantitative variables.
Pages 6668
Unit 2
Modeling Distributions of Data
Sept  Oct
Section
Concept
Objectives
Textbook Resources
2.1
Measuring Position
Use percentiles to locate individual values within distributions of data.
Pages 8586
2.1
Interpret a cumulative relative frequency graph.
Pages 8689
2.1
Find the standardized value (zscore) of an observation.
Pages 8991
2.1
Transforming Data
Describe the effect of adding, subtracting, multiplying by, or dividing by a constant on the shape, center, and spread of a distribution of data.
Pages 9297
2.2
Normal Distributions,
Use the 68–95–99.7 rule to estimate the percent of observations from a Normal distribution.
Pages 110114
2.2
Use the standard Normal distribution to calculate the proportion of values in a specified interval.
Pages 115119
2.2
Use the standard Normal distribution to determine a zscore from a percentile.
Pages 115119
2.2
Normal Distribution Calculations
Use Table A to find the percentile of a value from any Normal distribution.
Pages 119124
2.2
Make an appropriate graph to determine if a distribution is bellshaped.
Pages 119124
2.2
Use the 689599.7 rule to assess Normality of a data set.
Pages 124129
2.2
Interpret a Normal probability plot
Pages 124129
Unit 3
Describing Relationships
Oct  Nov
Section
Concept
Objectives
Textbook Resources
3.1
Interpreting scatterplots
Describe why it is important to investigate relationships between variables.
Pages 144146
3.1
Identify explanatory and response variables.
Pages 143144
3.1
Make a scatterplot to display the relationship between two quantitative variables.
Pages 144146
3.1
Describe the direction, form, and strength of the overall pattern of a scatterplot.
Pages 146150
3.1
Recognize outliers in a scatterplot.
Pages 146150
3.1
Linear Association
Know the basic properties of correlation.
Pages 150155
3.1
Calculate and interpret correlation in context.
Pages 150155
3.1
Explain how the correlation r is influenced by extreme observations.
Pages 155156
3.2
Leastsquares Regression Model
Interpret the slope and y intercept of a leastsquares regression line.
Pages 164167
3.2
Use the leastsquares regression line to predict y for a given x.
Pages 165167
3.2
Explain the dangers of extrapolation.
Pages 167
3.2
Residuals
Calculate and interpret residuals in context.
Pages 168169
3.2
Explain the concept of least squares.
Pages 169
3.2
Use technology to find a leastsquares regression line.
Pages 170171
3.2
Find the slope and intercept of the leastsquares regression line.
Pages 172174
3.2
The role of r2 in regression
Construct and interpret residual plots.
Pages 174177
3.2
Use the standard deviation of the residuals to assess how well the line fits the data.
Pages 177179
3.2
Use r2 to assess how well the line fits the data.
Pages 179181
3.2
Interpret the standard deviation of the residuals and r2 in context.
Pages 179181
3.2
Interpreting computer Outputs
Identify the equation of a leastsquares regression line from computer output.
Pages 182187
3.2
Explain why association doesn’t imply causation
Pages 182187
3.2
Recognize how the slope, y intercept, standard deviation of the residuals, and r2 are influenced by extreme observations.
Pages 187189
End of Quarter 1
Unit 4
Designing Studies
November
Section
Concept
Objectives
Textbook Resources
4.1
Sampling and Surveys
Identify the population and sample in a sample survey.
Pages 207208
4.1
Identify voluntary response samples and convenience samples.
Pages 208211
4.1
Describe how to use Table D to select a simple random sample (SRS).
Pages 211213
4.1
Other Sampling Methods
Distinguish a simple random sample from a stratified random sample or cluster sample.
Pages 215220
4.1
Inference for Sampling
Explain how undercoverage, nonresponse, and question wording can lead to bias in a sample survey.
Pages 221224
4.2
Observational Studies vs.
Experiments
Distinguish between an observational study and an experiment.
Pages 231232
4.2
Explain how a lurking variable in an observational study can lead to confounding.
Pages 232233
4.2
Identify the experimental units or subjects, explanatory variables (factors), treatments, and response variables in an experiment.
Pages 233236
4.2
Three
Principles of Experimental Design
Describe a completely randomized design for an experiment.
Pages 237241
4.2
Explain why random assignment is an important experimental design principle.
Pages 242
4.2
Inference for Experiments
Describe how to avoid the placebo effect in an experiment.
Pages 243
4.2
Explain the meaning and the purpose of blinding in an experiment.
Pages 244
4.2
Explain in context what “statistically significant” means.
Pages 244
4.2
Blocking, Matched Pairs Design
Distinguish between a completely randomized design and a randomized block design.
Pages 246248
4.2
Know when a matched pairs experimental design is appropriate and how to implement such a design.
Pages 249251
4.3
Scope of Inference
Determine the scope of inference for a statistical study.
Pages 261264
Unit 5
Probability
Nov  Dec
Section
Concept
Objectives
Textbook Resources
5.1
Probability
Interpret probability as a longrun relative frequency in context.
Pages 283288
5.1
Simulation
Use simulation to model chance behavior.
Pages 289292
5.2
Probability Models
Describe a probability model for a chance process.
Pages 299300
5.2
Use basic probability rules, including the complement rule and the addition rule for mutually exclusive events.
Pages 301303
5.2
Probability using Twoway tables and Venn diagrams
Use a Venn diagram to model a chance process involving two events.
Pages 303308
5.2
Use the general addition rule to calculate P(A union B)
Pages 303308
5.3
Conditional Probability
When appropriate, use a tree diagram to describe chance behavior.
Pages 312320
5.3
Use the general multiplication rule to solve probability questions.
Pages 317320
5.3
Determine whether two events are independent.
Pages 312320
5.3
Find the probability that an event occurs using a twoway table.
Pages 312320
5.3
Independent Events
Use the multiplication rule for
independent events to compute probabilities.
Pages 312320
5.3
Compute conditional probabilities.
Pages 324328
Unit 6
Random Variables
Dec  Jan
Section
Concept
Objectives
Textbook Resources
6.1
Expected Values
Use a probability distribution for random variable.
Pages 341342
6.1
Calculate the mean of a discrete random variable.
Pages 342346
6.1
Interpret the mean of a random variable in context.
Pages 342346
6.1
Standard Deviation
Calculate the standard deviation of a discrete random variable.
Pages 347348
6.1
Interpret the standard deviation of a random variable in context.
Pages 347348
6.2
Linear Transformations
Describe the effects of transforming a random variable.
Pages 358365
6.2
Combining Random Variables
Find the mean and standard deviation of the sum or difference of independent random variables.
Pages 366372
6.2
Determine whether two random variables are independent.
Pages 365
6.2
Find probabilities involving the sum or difference of independent Normal random variables.
Pages 372
6.3
Binomial Probabilities
Determine whether the conditions for a binomial random variable are met.
Pages 383384
6.3
Compute and interpret probabilities involving binomial distributions.
Pages 384390
6.3
Mean and Standard Deviation of a
Binomial Distribution
Calculate the mean and standard deviation of a binomial random variable.
Pages 390397
6.3
Geometric Random Variables
Find probabilities involving geometric random variables.
Pages 397401
End of Quarter 2
Unit 7
Sampling Distributions
January
Section
Concept
Objectives
Textbook Resources
7.1
Parameters and Statistics
Distinguish between a parameter and a statistic.
Pages 416
7.1
Sampling Variability
Understand the definition of a sampling distribution.
Pages 417420
7.1
Distinguish between population distribution, sampling distribution, and the distribution of sample data.
Pages 417420
7.1
Determine whether a statistic is an unbiased estimator of a population parameter.
Pages 421424
7.1
Understand the relationship between sample size and the variability of an estimator.
Pages 425427
7.2
Sampling Distribution
Find the mean and standard deviation of the sampling distribution of a sample proportion.
Pages 432436
7.2
Check whether the 10% and Normal conditions are met in a given setting.
Pages 432436
7.2
Use Normal approximation to calculate probabilities involving phat .
Pages 437438
7.2
Use the sampling distribution of phat to evaluate a claim about a population proportion.
Pages 432438
7.3
The Sampling Distribution Statistic
Find the mean and standard deviation of the sampling distribution of a sample mean xbar from an SRS of size n.
Pages 444
7.3
Calculate probabilities involving a sample mean xbar when the population distribution is Normal.
Pages 445448
7.3
The Central Limit Theorem
Explain how the shape of the sampling distribution of xbar is related to the shape of the population distribution.
Pages 449452
7.3
Use the central limit theorem to help find probabilities involving a sample mean xbar .
Pages 449452
Unit 8
Estimating with Confidence
Jan  Feb
Section
Concept
Objectives
Textbook Resources
8.1
Confidence Interval
Interpret a confidence level in context.
Pages 469480
8.1
Understand that a confidence interval gives a range of plausible values for the parameter.
Pages 469480
8.1
Constructing a Confidence
Understand why each of the three inference conditions—Random, Normal, and Independent—is important.
Pages 478479
8.2
Construct and interpret a confidence interval for a population proportion.
Pages 485490
8.2
Determine critical values for calculating a confidence interval using a table or your calculator.
Pages 485490
8.2
The FourStep Process
Carry out the steps in constructing a confidence interval for a population proportion.
Pages 490492
8.2
Determine the sample size required to obtain a level C confidence interval for a population proportion with a specified margin of error.
Pages 493
8.2
Understand how the margin of error of a confidence interval changes with the sample size and the level of confidence C.
Pages 491
8.2
Understand why each of the three inference conditions—Random, Normal, and Independent—is important.
Pages 490491
8.3
Constructing a
Confidence Interval for μ
Construct and interpret a confidence interval for a population mean.
Pages 499516
8.3
Determine the sample size required to obtain a level C confidence interval for a population mean with a specified margin of error.
Pages 500
8.3
Carry out the steps in constructing a confidence interval for a population mean.
Pages 507416
8.3
Confidence Intervals for μ on the Calculator
Understand why each of the three inference conditions—Random, Normal, and Independent—is important.
Pages 508
Unit 9
Testing a Claim
February
Section
Concept
Objectives
Textbook Resources
9.1
Significance Test
State correct hypotheses for a significance test about a population proportion or mean.
Pages 531532
9.1
Interpret Pvalues in context.
Pages 533534
9.1
Type I and Type II Errors
Interpret a Type I error and a Type II error in context.
Pages 538
9.1
Understand the relationship between the significance level of a test, P(Type II error), and power.
Pages 538542
9.2
The OneSample z Test for a Proportion
Check conditions for carrying out a test about a population proportion.
Pages 549555
9.2
If conditions are met, conduct a significance test about a population proportion.
Pages 549
9.2
TwoSided Tests
Use a confidence interval to draw a conclusion for a twosided test about a population proportion.
Pages 556557
9.3
The OneSample t Test
Check conditions for carrying out a test about a population mean
Pages 565570
9.3
If conditions are met, conduct a onesample t test about a population mean μ .
Pages 570574
9.3
Use a confidence interval to draw a conclusion for a twosided test about a population mean.
Pages 574577
9.3
Confidence Intervals for OneSample t Test
Recognize paired data and use onesample t procedures to perform significance tests for such data.
Pages 577581
End of Quarter 3
Unit 10
Comparing Two Populations or Groups
Feb  Mar
Section
Concept
Objectives
Textbook Resources
10.1
The Sampling Distribution for Difference Between Two Proportions
Describe the characteristics of the sampling distribution of phat1 − phat 2
Pages 604608
10.1
Calculate probabilities using the sampling distribution of phat1 − phat 2
Pages 608611
10.1
Determine whether the conditions for performing inference are met.
Pages 608611
10.1
Construct and interpret a confidence interval to compare two proportions.
Pages 608611
10.1
Significance Tests for p1 – p2
Perform a significance test to compare two proportions
Pages 611615
10.1
Interpret the results of inference procedures in a randomized experiment.
Pages 615619
10.2
The Sampling Distribution of a Difference Between Two Means
Describe the characteristics of the sampling distribution of xbar1 − xbar 2
Pages 628633
10.2
Calculate probabilities using the sampling distribution of xbar1 − xbar 2
Pages 628633
10.2
The TwoSample tStatistic
Determine whether the conditions for performing inference are met.
Pages 633634
10.2
Use twosample t procedures to compare two means based on summary statistics.
Pages 634638
10.2
Use twosample t procedures to compare two means from raw data.
Pages 634638
10.2
Interpret standard computer output for two sample tprocedures.
Pages 634638
10.2
Significance Tests for
xbar1 − xbar 2Perform a significance test to compare two means.
Pages 638644
10.2
Check conditions for using twosample t procedures in a randomized experiment.
Pages 644649
10.2
Interpret the results of inference procedures in a randomized experiment.
Pages 644649
Unit 11
Inference for Distributions of Categorical Data
March  April
Section
Concept
Objectives
Textbook Resources
11.1
Chi Square Tests
Compute expected counts, conditional distributions, and contributions to the chisquare statistic.
Pages 678685
11.1
The ChiSquare GoodnessofFit
Check the Random, Large sample size, and Independent conditions before performing a chisquare
test.
Pages 685
11.1
Use a chisquare goodnessoffit test to determine whether sample data are consistent with a specified distribution of a categorical variable.
Pages 685690
11.1
Examine individual components of the chisquare statistic as part of a followup analysis.
Pages 690
11.2
Comparing Distributions of a
Categorical Variable
Check the Random, Large sample size, and Independent conditions before performing a chisquare test.
Pages 696699
11.2
Use a chisquare test for homogeneity to determine whether the distribution of a categorical variable differs for several populations or treatments.
Pages 703709
11.2
Interpret computer output for a chisquare test based on a twoway table.
Pages 703709
11.2
Examine individual components of the chisquare statistic as part of a followup analysis.
Pages 709
11.2
Show that the twosample z test for comparing two proportions and the chisquare test for a 2 by2 twoway table give equivalent results.
Pages 709713
11.2
The ChiSquare Test of Association/Independence
Check the Random, Large sample size, and Independent conditions before performing a chisquare test.
Pages 713
11.2
Use a chisquare test of association/independence to determine whether there is convincing evidence of an association between two categorical variables.
Pages 714718
11.2
Interpret computer output for a chisquare test based on a twoway table.
Pages 714718
11.2
Examine individual components of the chisquare statistic as part of a followup analysis.
Pages 718719
Unit 12
More About Regression
April  May
Section
Concept
Objectives
Textbook Resources
12.1
The Sampling Distribution of b
Check conditions for performing inference about the slope b of the population regression line.
Pages 739743
12.1
Constructing a Confidence Interval for the Slope
Interpret computer output from a leastsquares regression analysis.
Pages 747751
12.1
Construct and interpret a confidence interval for the slope b of the population regression line.
Pages 747751
12.1
Performing a Significance Test for
the Slope
Perform a significance test about the slope b of a population regression line.
Pages 751757
12.2
Transforming with Powers and Roots
Use transformations involving powers and roots to achieve linearity for a relationship between two variables.
Pages 768771
12.2
Make predictions from a leastsquares regression line involving transformed data.
Pages 768771
12.2
Transforming with Logarithms
Use transformations involving logarithms to achieve linearity for a relationship between two variables.
Pages 771784
12.2
Make predictions from a leastsquares regression line involving transformed data.
Pages 771784
12.2
Determine which of several transformations does a better job of producing a linear relationship.
Pages 771784