Semester 1 AP Stats Topics by Chapter
Chapter 1
*Big ideas for solving statistical problems: Plot you data (Dotplot, Stemplot, Histogram)
Interpret what you see (Shape, Center, Spread, Outliers)
Choose numerical summary (𝑥̅ & 𝑠 , or Five Number Summary
-Create dotplot, stemplot, histograms, and boxplots
-Evaluate overall pattern of distribution using Center, Shape, and Spread
-Calculate mean, median, mode, 𝑄1 , 𝑄3 , outliers, range
-Read and sketch timeplots
-Median is more resistant than the mean, recognize skewness in a distribution.
-Calculate and graph with boxplot 5 number summary
-Effect of linear transformation on measures of center and spread and describe changes in units
-Compare distribution of categorical data: side-by-side boxplots, back-to-back stemplots
-Create two-way tables
-Marginal distributions vs. Conditional distributions
-Simpson’s Paradox
Chapter 2
*Describing an individual value’s location in a distribution and modeling distributions with density curves
-Find and interpret z-scores
-Use percentiles to locate individual values within distributions
-Areas under a density curve represent proportions of all observations, total area=1
-Mean and median both lie at the center of a symmetric density curve; mean moves farther toward the long tail of a
skewed curve
-Shape of normal curve; determine if distribution is normal from histogram
-68-95-99.7 Rule
-Calculate propotion of values in a specified range using 𝜇 and 𝜎 and Table A
Chapter 3
*Relations between two quantitative variables
-Quantitative or categorical?
-Explanatory and response variables?
- Scatterplot (explanatory on horizontal scale): Direction, form and strength of overall pattern
-Positive/Negative association, linear?, outliers?
-Calculate correlation 𝑟 and line of regression (least squares)using the calculator
- 𝑟 measures strength and direction of linear relationships only; −1 ≤ 𝑟 ≤ 1, 𝑟 = ±1 only for perfectly straight line
relations; 𝑟 moves away from 0 toward ±1 as linear relationship gets stronger
-Slope 𝑏, y-intercept 𝑎, in the regression line 𝑦̂ = 𝑎 + 𝑏𝑥
-Use regression line to predict values within the given range of data
-Extrapolation
-Calculate and plot residuals
-𝑟 and regression line can be strongly influenced by a few extreme observations
-Lurking Variables
Chapter 5
*Designing experiments and sampling – collecting data
-Identify population and recognize bias
-Select simple random sample (SRS) using tables or calculators
-Cluster sampling vs other sampling
-Recognize undercoverage and nonresponse, and wording as examples of error in sample
-Observational or experiment; recognize bias, lurking varibles
-Outline a design of a completely randomized experiment
-Identify factors, treatments, response variables, and experimental units/subjects in an experiment
-Placebo effect and double-blind technique
-Recognize block design and matched pairs design and when to use them
Chapter 6
*Probability
-Construct and run simulations (random number table or calculator)
-Sample space, multiplication principle, Venn diagrams, Tree diagrams for simple probabilities
- Know probability rules and how to apply them
-Two events are disjoint, complementary, or independent?
-General Addition rule, multiplication rule for independent events
-“And” vs “Or” situations
-Conditional Probability: understand, calculate
Chapter 7
*Random variable defines what is counted or measured in applications
-Difference between discrete and continuous random variable: tables and histograms for each
-Normal Random Variable - Normal table
-Calculate mean and variance of discrete random variables; expected value = mean
-Simulations and law of large numbers to approximate mean of a distributions
-Rules for means and variances to solve problems involving sums, differences and linear combinations