Unit 4 of 6

Problem-Solving and Data Analysis

  • 9 lessons
  • Parts 75 to 92

This unit reads data the way the SAT presents it, in tables, bar graphs, histograms, box plots and scatterplots. It covers mean, median, weighted averages, spread and standard deviation, and line and curve models for predictions.

Probability from two-way tables and conditional probability follow, and the unit ends with statistical reasoning about samples, margins of error, and what observational studies and experiments can and cannot show.

Every lesson is a pair of videos. The theory part explains the idea and the practice part works through problems. Each lesson page has the definitions and an example for every key term.

Data and Probability

  1. Reading Data Displays

    How to read frequencies, dot plots, histograms and box plots using their labeled scales, and how to tell the exact values a display shows from the information it groups or hides.

    Theory part 75Practice part 76

  2. Mean, Median and Weighted Averages

    How to compute a mean from totals and counts, find a median from ordered positions, weight group means by group sizes, and predict how one extreme value moves the mean and the median.

    Theory part 77Practice part 78

  3. Spread, Outliers and Standard Deviation

    How range and standard deviation measure how spread out data are, why an outlier widens both, and what adding a constant or multiplying every value does to the mean and the standard deviation.

    Theory part 79Practice part 80

  4. Scatterplots, Models and Predictions

    How to read a scatterplot, interpret the slope, intercept and residuals of a fitted model, and judge how far a prediction from that model can be trusted.

    Theory part 81Practice part 82

  5. Probability and Two-Way Tables

    How to find a probability as favorable outcomes over the correct total, read two-way tables, use complements and unions without double counting, and compute probability from area.

    Theory part 83Practice part 84

  6. Conditional Probability

    How a given condition shrinks the reference group, how to compute and reverse a conditional probability from a table, and how to test independence with actual numbers.

    Theory part 85Practice part 86

Statistical Reasoning

  1. Samples, Populations and Bias

    How a random sample lets you estimate a population proportion or mean, why the estimate is never exact, and how the way a sample is chosen limits whom the results describe.

    Theory part 87Practice part 88

  2. Margin of Error and Interpreting Estimates

    How to read an estimate with its margin of error as a range of plausible values, why percentage points differ from percent, and how sample size and confidence level change the width.

    Theory part 89Practice part 90

  3. Experiments, Observations and Causal Claims

    How to tell an observational study from a randomized experiment, why random assignment supports cause and effect while random sampling supports generalization, and how confounding misleads.

    Theory part 91Practice part 92