Statistics and Probability | Khan Academy

Khan Academy: Statistics and Probability Course Overview

This course provides a comprehensive curriculum covering foundational to advanced statistical concepts, organized into 16 units.

• Core Data Analysis:
  • Categorical Data: Analyzing variables, frequency tables (two-way/relative), and marginal/conditional distributions.
  • Quantitative Data: Creating and interpreting dot plots, histograms, stem-and-leaf plots, and box plots.
  • Summarizing Data: Calculating mean, median, mode, interquartile range (IQR), standard deviation, variance, and identifying outliers.
• Modeling and Relationships:
  • Distributions: Z-scores, percentiles, density curves, and the empirical rule for normal distributions.
  • Bivariate Data: Scatter plots, correlation coefficients, lines of best fit, residuals, and linear regression models.
• Study Design and Probability:
  • Study Design: Sampling methods, random samples, experimental design, and statistical inference.
  • Probability: Simple and compound events, independent/dependent events, conditional probability, and Venn diagrams.
  • Counting: Permutations and combinations.
• Advanced Statistical Inference:
  • Random Variables: Binomial and geometric distributions, expected value, and probability models.
  • Sampling Distributions: Central Limit Theorem, sample proportions, and sample means.
  • Confidence Intervals: Z-intervals for proportions and t-intervals for means.
  • Significance Testing: Hypothesis testing (null/alternative), P-values, Type I/II errors, and t-tests.
  • Categorical Inference: Chi-square tests (goodness-of-fit and two-way tables).
• Additional Topics:
  • The course includes advanced modules on two-sample inference, advanced regression, and Analysis of Variance (ANOVA).
• Structure: Each unit typically includes instructional content, practice exercises, and unit tests to track mastery.