Math Ladder · High school · Grade 12

Probability and Statistics

Describe data, model chance with probability rules and distributions, and draw careful conclusions with confidence intervals and tests.

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58 topics in 8 units. Builds on Algebra 2. Leads to Discrete Math and Probability. Not sure this is the right course? Find your rung.

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Unit 1 Describing Data

9 topics

Display one-variable data and summarize its center, spread and shape.

  1. Categorical and Quantitative Variables
  2. Displaying Categorical Data
  3. Histograms and Shape
  4. Mean, Median and Resistance
  5. Standard Deviation
  6. Five-Number Summary and Outliers
  7. Comparing Distributions
  8. z-Scores and Percentiles
  9. Shifting and Scaling Data

Unit 2 The Normal Distribution

3 topics

Use the normal model to find proportions and percentiles.

  1. The Normal Curve and the 68-95-99.7 Rule
  2. Areas under the Normal Curve
  3. Finding Values from Percentiles

Unit 3 Two-Variable Data

9 topics

Describe association, fit least-squares lines, and judge a model with residuals.

  1. Describing Scatterplots
  2. The Correlation Coefficient
  3. The Least-Squares Regression Line
  4. Interpreting Slope and Intercept
  5. Residuals and Residual Plots
  6. r² and the Quality of Fit
  7. Outliers and Influential Points
  8. Fitting Exponential and Power Models
  9. Correlation, Causation and Lurking Variables

Unit 4 Collecting Data

5 topics

Choose samples, avoid bias, and design experiments.

  1. Sampling Methods
  2. Bias in Sampling and Surveys
  3. Observational Studies and Experiments
  4. Designing Experiments
  5. Evaluating Statistical Reports

Unit 5 Probability Rules

10 topics

Use the addition and multiplication rules, conditional probability and counting.

  1. Events, Unions, Intersections and Complements
  2. The Addition Rule
  3. Conditional Probability
  4. Conditional Probability from Two-Way Tables
  5. Independent Events
  6. The General Multiplication Rule
  7. Bayes' Rule
  8. Permutations
  9. Combinations
  10. Probability with Counting

Unit 6 Random Variables

8 topics

Describe random outcomes with distributions, means and standard deviations.

  1. Discrete Random Variables
  2. Expected Value
  3. Standard Deviation of a Random Variable
  4. Sums and Differences of Random Variables
  5. The Binomial Distribution
  6. The Geometric Distribution
  7. Continuous Random Variables
  8. Decisions with Expected Value

Unit 7 Sampling Distributions

3 topics

See how statistics vary from sample to sample.

  1. Is the Model Consistent? Simulation
  2. Sampling Distribution of a Proportion
  3. Sampling Distribution of a Mean and the CLT

Unit 8 Inference

11 topics

Estimate with confidence intervals and test claims with significance tests.

  1. Confidence Intervals for a Proportion
  2. Margin of Error and Sample Size
  3. Confidence Intervals for a Mean
  4. The Logic of Significance Tests
  5. Testing a Claim about a Proportion
  6. Testing a Claim about a Mean
  7. Type I and Type II Errors and Power
  8. Comparing Two Treatments by Randomization
  9. Two-Sample Intervals and Tests
  10. Chi-Square Tests
  11. Inference for the Slope of a Regression Line
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