AP Statistics

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 2-7
Intro		Classify variables as categorical or quantitative.	Pages 2-7
1.1	Bar Graphs and Pie Charts	Identify units of measurement for a quantitative variable.	Pages 8-10
1.1		Make a bar graph of the distribution of a categorical variable	Pages 8-10
1.1		Recognize when a pie chart can and cannot be used.	Pages 8-10
1.1		Identify what makes some graphs deceptive.	Pages 11-12
1.1	Two-Way Tables	From a two-way table of counts, answer questions involving marginal and conditional distributions.	Pages 12-14
1.1		Describe the relationship between two categorical variables	Pages 14-15
1.1		Construct bar graphs to display the relationship between two categorical variables.	Pages 16-19
1.2	Comparing Distributions	Make a dot-plot or stem-plot to display small sets of data.	Pages 27-28
1.2		Describe the overall pattern (shape, center, spread) of a distribution	Pages 29-32
1.2		Identify the shape of a distribution from a dot-plot, stem-plot, or histogram as roughly symmetric or skewed.	Pages 29-32
1.2	Histograms	Make a histogram with a reasonable choice of classes.	Pages 35-41
1.2		Interpret histograms.	Pages 35-37
1.3	Measuring Centers Identifying Outliers	Calculate and interpret measures of center (mean, median) in context	Pages 50-55
1.3		Calculate and interpret measures of spread (IQR) in context	Pages 55-57
1.3		Identify outliers using the 1.5 × IQR rule.	Pages 57-59
1.3	Five Number Summary and Standard Deviation	Make a boxplot.	Pages 59-61
1.3		Calculate and interpret measures of spread (standard deviation)	Pages 62-66
1.3		Select appropriate measures of center and spread	Pages 66-68
1.3		Use appropriate graphs and numerical summaries to compare distributions of quantitative variables.	Pages 66-68
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 85-86
2.1		Interpret a cumulative relative frequency graph.	Pages 86-89
2.1		Find the standardized value (z-score) of an observation.	Pages 89-91
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 92-97
2.2	Normal Distributions,	Use the 68–95–99.7 rule to estimate the percent of observations from a Normal distribution.	Pages 110-114
2.2		Use the standard Normal distribution to calculate the proportion of values in a specified interval.	Pages 115-119
2.2		Use the standard Normal distribution to determine a z-score from a percentile.	Pages 115-119
2.2	Normal Distribution Calculations	Use Table A to find the percentile of a value from any Normal distribution.	Pages 119-124
2.2		Make an appropriate graph to determine if a distribution is bell-shaped.	Pages 119-124
2.2		Use the 68-95-99.7 rule to assess Normality of a data set.	Pages 124-129
2.2		Interpret a Normal probability plot	Pages 124-129
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 144-146
3.1		Identify explanatory and response variables.	Pages 143-144
3.1		Make a scatterplot to display the relationship between two quantitative variables.	Pages 144-146
3.1		Describe the direction, form, and strength of the overall pattern of a scatterplot.	Pages 146-150
3.1		Recognize outliers in a scatterplot.	Pages 146-150
3.1	Linear Association	Know the basic properties of correlation.	Pages 150-155
3.1		Calculate and interpret correlation in context.	Pages 150-155
3.1		Explain how the correlation r is influenced by extreme observations.	Pages 155-156
3.2	Least-squares Regression Model	Interpret the slope and y intercept of a least-squares regression line.	Pages 164-167
3.2		Use the least-squares regression line to predict y for a given x.	Pages 165-167
3.2		Explain the dangers of extrapolation.	Pages 167
3.2	Residuals	Calculate and interpret residuals in context.	Pages 168-169
3.2		Explain the concept of least squares.	Pages 169
3.2		Use technology to find a least-squares regression line.	Pages 170-171
3.2		Find the slope and intercept of the least-squares regression line.	Pages 172-174
3.2	The role of r2 in regression	Construct and interpret residual plots.	Pages 174-177
3.2		Use the standard deviation of the residuals to assess how well the line fits the data.	Pages 177-179
3.2		Use r2 to assess how well the line fits the data.	Pages 179-181
3.2		Interpret the standard deviation of the residuals and r2 in context.	Pages 179-181
3.2	Interpreting computer Outputs	Identify the equation of a least-squares regression line from computer output.	Pages 182-187
3.2		Explain why association doesn’t imply causation	Pages 182-187
3.2		Recognize how the slope, y intercept, standard deviation of the residuals, and r2 are influenced by extreme observations.	Pages 187-189
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 207-208
4.1		Identify voluntary response samples and convenience samples.	Pages 208-211
4.1		Describe how to use Table D to select a simple random sample (SRS).	Pages 211-213
4.1	Other Sampling Methods	Distinguish a simple random sample from a stratified random sample or cluster sample.	Pages 215-220
4.1	Inference for Sampling	Explain how under-coverage, nonresponse, and question wording can lead to bias in a sample survey.	Pages 221-224
4.2	Observational Studies vs. Experiments	Distinguish between an observational study and an experiment.	Pages 231-232
4.2		Explain how a lurking variable in an observational study can lead to confounding.	Pages 232-233
4.2		Identify the experimental units or subjects, explanatory variables (factors), treatments, and response variables in an experiment.	Pages 233-236
4.2	Three Principles of Experimental Design	Describe a completely randomized design for an experiment.	Pages 237-241
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 246-248
4.2		Know when a matched pairs experimental design is appropriate and how to implement such a design.	Pages 249-251
4.3	Scope of Inference	Determine the scope of inference for a statistical study.	Pages 261-264
Unit 5	Probability		Nov - Dec
Section	Concept	Objectives	Textbook Resources
5.1	Probability	Interpret probability as a long-run relative frequency in context.	Pages 283-288
5.1	Simulation	Use simulation to model chance behavior.	Pages 289-292
5.2	Probability Models	Describe a probability model for a chance process.	Pages 299-300
5.2		Use basic probability rules, including the complement rule and the addition rule for mutually exclusive events.	Pages 301-303
5.2	Probability using Two-way tables and Venn diagrams	Use a Venn diagram to model a chance process involving two events.	Pages 303-308
5.2		Use the general addition rule to calculate P(A union B)	Pages 303-308
5.3	Conditional Probability	When appropriate, use a tree diagram to describe chance behavior.	Pages 312-320
5.3		Use the general multiplication rule to solve probability questions.	Pages 317-320
5.3		Determine whether two events are independent.	Pages 312-320
5.3		Find the probability that an event occurs using a two-way table.	Pages 312-320
5.3	Independent Events	Use the multiplication rule for independent events to compute probabilities.	Pages 312-320
5.3		Compute conditional probabilities.	Pages 324-328
Unit 6	Random Variables		Dec - Jan
Section	Concept	Objectives	Textbook Resources
6.1	Expected Values	Use a probability distribution for random variable.	Pages 341-342
6.1		Calculate the mean of a discrete random variable.	Pages 342-346
6.1		Interpret the mean of a random variable in context.	Pages 342-346
6.1	Standard Deviation	Calculate the standard deviation of a discrete random variable.	Pages 347-348
6.1		Interpret the standard deviation of a random variable in context.	Pages 347-348
6.2	Linear Transformations	Describe the effects of transforming a random variable.	Pages 358-365
6.2	Combining Random Variables	Find the mean and standard deviation of the sum or difference of independent random variables.	Pages 366-372
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 383-384
6.3		Compute and interpret probabilities involving binomial distributions.	Pages 384-390
6.3	Mean and Standard Deviation of a Binomial Distribution	Calculate the mean and standard deviation of a binomial random variable.	Pages 390-397
6.3	Geometric Random Variables	Find probabilities involving geometric random variables.	Pages 397-401
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 417-420
7.1		Distinguish between population distribution, sampling distribution, and the distribution of sample data.	Pages 417-420
7.1		Determine whether a statistic is an unbiased estimator of a population parameter.	Pages 421-424
7.1		Understand the relationship between sample size and the variability of an estimator.	Pages 425-427
7.2	Sampling Distribution	Find the mean and standard deviation of the sampling distribution of a sample proportion.	Pages 432-436
7.2		Check whether the 10% and Normal conditions are met in a given setting.	Pages 432-436
7.2		Use Normal approximation to calculate probabilities involving p-hat .	Pages 437-438
7.2		Use the sampling distribution of p-hat to evaluate a claim about a population proportion.	Pages 432-438
7.3	The Sampling Distribution Statistic	Find the mean and standard deviation of the sampling distribution of a sample mean x-bar from an SRS of size n.	Pages 444
7.3		Calculate probabilities involving a sample mean x-bar when the population distribution is Normal.	Pages 445-448
7.3	The Central Limit Theorem	Explain how the shape of the sampling distribution of x-bar is related to the shape of the population distribution.	Pages 449-452
7.3		Use the central limit theorem to help find probabilities involving a sample mean x-bar .	Pages 449-452
Unit 8	Estimating with Confidence		Jan - Feb
Section	Concept	Objectives	Textbook Resources
8.1	Confidence Interval	Interpret a confidence level in context.	Pages 469-480
8.1		Understand that a confidence interval gives a range of plausible values for the parameter.	Pages 469-480
8.1	Constructing a Confidence	Understand why each of the three inference conditions—Random, Normal, and Independent—is important.	Pages 478-479
8.2		Construct and interpret a confidence interval for a population proportion.	Pages 485-490
8.2		Determine critical values for calculating a confidence interval using a table or your calculator.	Pages 485-490
8.2	The Four-Step Process	Carry out the steps in constructing a confidence interval for a population proportion.	Pages 490-492
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 490-491
8.3	Constructing a Confidence Interval for μ	Construct and interpret a confidence interval for a population mean.	Pages 499-516
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 507-416
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 531-532
9.1		Interpret P-values in context.	Pages 533-534
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 538-542
9.2	The One-Sample z Test for a Proportion	Check conditions for carrying out a test about a population proportion.	Pages 549-555
9.2		If conditions are met, conduct a significance test about a population proportion.	Pages 549
9.2	Two-Sided Tests	Use a confidence interval to draw a conclusion for a two-sided test about a population proportion.	Pages 556-557
9.3	The One-Sample t Test	Check conditions for carrying out a test about a population mean	Pages 565-570
9.3		If conditions are met, conduct a one-sample t test about a population mean μ .	Pages 570-574
9.3		Use a confidence interval to draw a conclusion for a two-sided test about a population mean.	Pages 574-577
9.3	Confidence Intervals for One-Sample t Test	Recognize paired data and use one-sample t procedures to perform significance tests for such data.	Pages 577-581
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 p-hat1 − p-hat 2	Pages 604-608
10.1		Calculate probabilities using the sampling distribution of p-hat1 − p-hat 2	Pages 608-611
10.1		Determine whether the conditions for performing inference are met.	Pages 608-611
10.1		Construct and interpret a confidence interval to compare two proportions.	Pages 608-611
10.1	Significance Tests for p1 – p2	Perform a significance test to compare two proportions	Pages 611-615
10.1		Interpret the results of inference procedures in a randomized experiment.	Pages 615-619
10.2	The Sampling Distribution of a Difference Between Two Means	Describe the characteristics of the sampling distribution of x-bar1 − x-bar 2	Pages 628-633
10.2		Calculate probabilities using the sampling distribution of x-bar1 − x-bar 2	Pages 628-633
10.2	The Two-Sample t-Statistic	Determine whether the conditions for performing inference are met.	Pages 633-634
10.2		Use two-sample t procedures to compare two means based on summary statistics.	Pages 634-638
10.2		Use two-sample t procedures to compare two means from raw data.	Pages 634-638
10.2		Interpret standard computer output for two sample t-procedures.	Pages 634-638
10.2	Significance Tests for x-bar1 − x-bar 2	Perform a significance test to compare two means.	Pages 638-644
10.2		Check conditions for using two-sample t procedures in a randomized experiment.	Pages 644-649
10.2		Interpret the results of inference procedures in a randomized experiment.	Pages 644-649
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 chi-square statistic.	Pages 678-685
11.1	The Chi-Square Goodness-of-Fit	Check the Random, Large sample size, and Independent conditions before performing a chi-square test.	Pages 685
11.1		Use a chi-square goodness-of-fit test to determine whether sample data are consistent with a specified distribution of a categorical variable.	Pages 685-690
11.1		Examine individual components of the chi-square statistic as part of a follow-up analysis.	Pages 690
11.2	Comparing Distributions of a Categorical Variable	Check the Random, Large sample size, and Independent conditions before performing a chi-square test.	Pages 696-699
11.2		Use a chi-square test for homogeneity to determine whether the distribution of a categorical variable differs for several populations or treatments.	Pages 703-709
11.2		Interpret computer output for a chi-square test based on a two-way table.	Pages 703-709
11.2		Examine individual components of the chi-square statistic as part of a follow-up analysis.	Pages 709
11.2		Show that the two-sample z test for comparing two proportions and the chi-square test for a 2- by-2 two-way table give equivalent results.	Pages 709-713
11.2	The Chi-Square Test of Association/Independence	Check the Random, Large sample size, and Independent conditions before performing a chi-square test.	Pages 713
11.2		Use a chi-square test of association/independence to determine whether there is convincing evidence of an association between two categorical variables.	Pages 714-718
11.2		Interpret computer output for a chi-square test based on a two-way table.	Pages 714-718
11.2		Examine individual components of the chi-square statistic as part of a follow-up analysis.	Pages 718-719
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 739-743
12.1	Constructing a Confidence Interval for the Slope	Interpret computer output from a least-squares regression analysis.	Pages 747-751
12.1		Construct and interpret a confidence interval for the slope b of the population regression line.	Pages 747-751
12.1	Performing a Significance Test for the Slope	Perform a significance test about the slope b of a population regression line.	Pages 751-757
12.2	Transforming with Powers and Roots	Use transformations involving powers and roots to achieve linearity for a relationship between two variables.	Pages 768-771
12.2		Make predictions from a least-squares regression line involving transformed data.	Pages 768-771
12.2	Transforming with Logarithms	Use transformations involving logarithms to achieve linearity for a relationship between two variables.	Pages 771-784
12.2		Make predictions from a least-squares regression line involving transformed data.	Pages 771-784
12.2		Determine which of several transformations does a better job of producing a linear relationship.	Pages 771-784