AP Exams (Advanced Placement) AP Mathematics and Computer Science (Statistics & CS) Syllabus

AP Mathematics and Computer Science (Statistics & CS) syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for AP Mathematics and Computer Science (Statistics & CS) in AP Exams (Advanced Placement), not a summary of it.

1. 1

   AP Statistics: Exploring Data

   3 topics

   • Describing Distributions
     • Shape, center, and spread
     • Outliers and graphical displays
   • Summarizing Quantitative Data
     • Mean, median, and standard deviation
     • Z-scores and the normal model
   • Two-Variable Data
     • Correlation and least-squares regression
     • Residuals and influential points
2. 2

   AP Statistics: Probability and Sampling

   3 topics

   • Sampling and Experimental Design
     • Random sampling methods
     • Experiments vs observational studies
   • Probability Rules
     • Conditional probability and independence
   • Random Variables and Distributions
     • Binomial and geometric distributions
     • Sampling distributions and CLT
3. 3

   AP Statistics: Inference

   3 topics

   • Confidence Intervals
     • Intervals for means and proportions
   • Hypothesis Testing
     • Significance tests for means and proportions
     • Type I/II errors and power
   • Chi-Square and Regression Inference
     • Goodness of fit and independence
     • Inference for slope
4. 4

   AP Computer Science A

   4 topics

   • Java Fundamentals
     • Primitive types and expressions
     • Boolean logic and conditionals
   • Objects and Classes
     • Writing classes and methods
     • Inheritance and polymorphism
   • Data Structures
     • Arrays and ArrayLists
     • 2D arrays
   • Algorithms and Recursion
     • Searching and sorting
     • Recursion
5. 5

   AP Computer Science Principles

   5 topics

   • Creative Development and Program Design
   • Data and Information
     • Binary and data representation
     • Data analysis and visualization
   • Algorithms and Programming
   • Computing Systems and Networks
     • The Internet and fault tolerance
   • Impact of Computing
     • Digital divide and ethics
     • Cybersecurity and privacy

AP Mathematics and Computer Science (Statistics & CS) flashcards for AP Exams (Advanced Placement)

25 of 65 cards from the AP Mathematics and Computer Science (Statistics & CS) deck — real questions with worked answers.

1. In statistics, what four features should you describe when summarizing the distribution of a quantitative variable?

   Shape, Center, Spread (Variability), and Unusual features such as outliers or gaps (remember SOCS / shape-outliers-center-spread).

2. What does it mean for a distribution to be skewed right (positively skewed), and how do the mean and median compare?

   The right tail is longer; most data cluster on the left. The mean is pulled toward the tail, so mean > median.

3. Distinguish between a categorical variable and a quantitative variable.

   A categorical variable places individuals into groups/labels (e.g., eye color); a quantitative variable takes numerical values for which arithmetic makes sense (e.g., height).

4. Which graphical displays are appropriate for categorical data versus quantitative data?

   Categorical: bar charts and pie charts. Quantitative: dotplots, stemplots, histograms, and boxplots.

5. How is the median found, and why is it resistant to outliers?

   The median is the middle value of ordered data (average of the two middle values if n is even). It depends only on the order/position of values, not their magnitude, so extreme values don't shift it.

6. State the formula for the sample standard deviation.

   s = sqrt( Σ(xᵢ − x̄)² / (n − 1) ); it is the square root of the variance and measures typical distance of values from the mean.

7. What are the five numbers in the five-number summary, and what does the IQR equal?

   Minimum, Q1, Median, Q3, Maximum. IQR = Q3 − Q1, the range of the middle 50% of the data.

8. State the 1.5 × IQR rule for identifying outliers.

   A value is an outlier if it is below Q1 − 1.5(IQR) or above Q3 + 1.5(IQR).

9. How does multiplying every data value by a constant a and adding b affect the mean and standard deviation?

   New mean = a·(mean) + b. New standard deviation = |a|·(SD) — adding b does not change spread; multiplying scales it.

10. What does a z-score measure, and what is its formula?

    A z-score gives how many standard deviations a value is from the mean: z = (x − x̄)/s (or (x − μ)/σ). It standardizes values for comparison.

11. When describing a scatterplot of two quantitative variables, what four characteristics should you mention?

    Direction (positive/negative), Form (linear/curved), Strength (how tight), and Unusual features/outliers — plus context.

12. What does the correlation coefficient r measure, and what is its range?

    r measures the strength and direction of a LINEAR relationship between two quantitative variables; it ranges from −1 to +1. It has no units and is not resistant to outliers.

13. Interpret the coefficient of determination r² in a regression context.

    r² is the proportion (fraction/percent) of the variation in the response variable y that is explained by the linear regression on the explanatory variable x.

14. In the least-squares regression equation ŷ = a + bx, how do you interpret the slope b?

    For each one-unit increase in x, the predicted value of y changes by b units (the slope is the predicted change in y per unit x).

15. What is a residual, and what does a residual plot with no pattern indicate?

    Residual = observed y − predicted ŷ. A residual plot with random scatter (no pattern) indicates a linear model is appropriate.

16. Distinguish between an observational study and an experiment.

    In an observational study you measure variables without imposing treatments; in an experiment you deliberately impose treatments on subjects to observe a response, allowing cause-and-effect conclusions.

17. Name the three principles of good experimental design.

    Control (compare treatments / hold other variables constant), Randomization (randomly assign treatments), and Replication (enough subjects to reduce chance variation).

18. Define a simple random sample (SRS).

    An SRS of size n is chosen so that every possible group of n individuals has an equal chance of being selected.

19. Compare stratified random sampling and cluster sampling.

    Stratified: divide population into similar groups (strata) and take an SRS from EACH stratum. Cluster: divide into groups (clusters), randomly select whole clusters, and sample everyone in them.

20. What is a confounding variable?

    A variable associated with both the explanatory variable and the response, so its effect on the response cannot be separated from the explanatory variable's effect.

21. State the complement rule and the general addition rule for probability.

    Complement: P(Aᶜ) = 1 − P(A). Addition: P(A or B) = P(A) + P(B) − P(A and B).

22. What does it mean for two events to be mutually exclusive (disjoint), and what does that imply for P(A and B)?

    They cannot occur at the same time; P(A and B) = 0, so P(A or B) = P(A) + P(B).

23. State the formula for conditional probability and the test for independence.

    P(A | B) = P(A and B) / P(B). Events A and B are independent if P(A | B) = P(A), equivalently P(A and B) = P(A)·P(B).

24. How do you find the mean (expected value) of a discrete random variable X?

    E(X) = μ = Σ [xᵢ · P(xᵢ)] — sum each value times its probability.

25. What four conditions define a binomial setting (BINS)?

    Binary outcomes (success/failure), Independent trials, fixed Number of trials n, and Same probability p of success on each trial.

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