How to automate AI workflows in Microsoft’s Azure and Fabric, despite marketing rebrands, and passing AI-900 & AI-102 certification exams.
AP Statistics is College Board’s most popular exam.
https://apstudents.collegeboard.org/courses/ap-Statistics
AP® Statistics gives students hands-on experience collecting, analyzing, graphing, and interpreting real-world data. They will learn to effectively design and analyze research studies by reviewing and evaluating real research examples taken from daily life. The next time they hear the results of a poll or study, they will know whether the results are valid. As the art of drawing conclusions from imperfect data and the science of real-world uncertainties, statistics plays an important role in many fields. The equivalent of an introductory college-level course, AP® Statistics prepares students for the AP exam and for further study in science, sociology, medicine, engineering, political science, geography, and business.
A. Selecting Statistical Methods = Select methods for collecting and/or analyzing data for statistical
inference.
B. Data Analysis = Describe patterns, trends, associations, and relationships in data.
C. Using Probability and Simulation = to describe probability distributions and define uncertainty in statistical inference. Explore random phenomena.
D. Statistical Argumentation = Develop an explanation or justify a conclusion using evidence from data,
definitions, or statistical inference. Use statistical reasoning to draw appropriate conclusions and justify claims.
REMEMBER: Graphing calculators (TI-85) are allowed during exams.
https://apcentral.collegeboard.org/courses/ap-statistics Exam Description PDF (Effective Fall 2020)
| Unit | Weight | Khan |
|---|---|---|
| 1. Exploring One-Variable Data | 15-23% | AP |
| 2. Exploring Two-Variable Data | 5-7% | AP |
| 3. Collecting Data | 12-15% | AP |
| 4. Probability, Random Variables, and Probability Distributions | 10-20% | AP |
| 5. Sampling Distributions | 7-12% | AP |
| 6. Inference for Categorical Data: Proportions | 12-15% | AP |
| 7. Inference for Quantitative Data: Means | 10-18% | AP |
| 8. Inference for Categorical Data: Chi-square | 2-5% | AP |
| 9. Inference for Quantitative Data: Slopes | 2-65% | AP |
| * Prepare for the 2022* AP Statistics Exam | - | AP |
The AP Statistics Exam is Thu, May 7, 2026 at 12 PM Local
see https://www.statsdirect.com/help/references/glossary.htm
| Symbol | Greek | Meaning |
|---|---|---|
| α | alpha | Significance level (Type I error rate) |
| β | Beta | Type II error rate (probability of false negative) |
| μ | mu | Population mean (average) |
| n | - | Sample size (N = population size) |
| σ | sigma | Population standard deviation |
| Var or s² | - | Variance (measure of dispersion) |
| P | - | Probability of an event or data sample |
| p̂ | hat | Sample proportion (estimate of population proportion) |
| R | - | Correlation coefficient (linear relationship strength) |
| t | - | Student’s t-statistic for small-sample inference |
| z | - | Standardized score or test statistic divided by SE |
| Term | Definition |
|---|---|
| Alternative hypothesis (H₁) | Hypothesis that there is a significant effect or difference |
| ANOVA | Analysis of variance; tests means across multiple groups |
| Chi-square test (χ²) | Test comparing observed and expected frequencies |
| Confidence Interval (CI) | Range estimating the true population parameter |
| Correlation | Strength and direction of relationship between two variables |
| Histogram | Graph displaying frequency distribution of data |
| Kurtosis | Measure of tail heaviness or peakedness of a distribution |
| Normal distribution | Bell-shaped distribution symmetric about the mean |
| Null hypothesis (H₀) | Initial assumption of no effect |
| Outlier | Data point that differs significantly from others |
| p-value | Probability of obtaining results as extreme as observed if H₀ is true |
| Population | Complete group from which samples are drawn |
| Random variable | Variable whose value is subject to randomness |
| Regression analysis | Method estimating relationships between dependent and independent variables |
| Sample | Subset drawn from a population to represent it in analysis |
| Skewness | Measure of asymmetry in the distribution |
| Standard deviation | Square root of variance; average distance from mean |
| Time series | Data collected over time at regular intervals |
| Variance | Average squared deviation from the mean; measures spread |
| Acronym | Full Form | Notes |
|---|---|---|
| ANOVA | Analysis of Variance | Compares group means |
| ANCOVA | Analysis of Covariance | Controls for covariates |
| BIC/AIC | Bayesian/ Akaike Information Criterion | Used for model selection |
| CI | Confidence Interval | Indicates estimate precision |
| CI95 | 95% Confidence Interval | Standard interval for hypothesis testing |
| df | Degrees of Freedom | Number of independent values minus constraints |
| IQR | Interquartile Range | Distance between 25th and 75th percentile (spread of middle 50%) |
| RMSE | Root Mean Square Error | Common measure of model accuracy |
| R² | Coefficient of Determination | Percentage of variance explained by model |
| SD | Standard deviation of a sample | |
| SE | Standard error (uncertainty around sample) | |
| SEM | Standard Error of the Mean | Average variability of sample means |
| SS | Sum of Squares | Total variation in data |
| SRS | simple random sample | a sample taken so that each member and set of [n] members has an equal chance of being in the sample. |
https://www.khanacademy.org/math/ap-statistics
Unit 1: Exploring categorical data
Unit 2: Exploring one-variable quantitative data: Displaying and describing
Describing the distribution of a quantitative variable: Exploring one-variable quantitative data: Displaying and describing
Unit 3: Exploring one-variable quantitative data: Summary statistics
Measuring variability in quantitative data: Exploring one-variable quantitative data: Summary statistics
Unit 4: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution
Density curves: Exploring one-variable quantitative data: Percentiles, z-scores, and the normal distribution
Unit 5: Exploring two-variable quantitative data
Residuals: Exploring two-variable quantitative data
Unit 6: Collecting data
Random sampling and data collection: Collecting data
Unit 7: Probability
Conditional probability: Probability
Unit 8: Random variables and probability distributions
Transforming random variables: Random variables and probability distributions
Unit 9: Sampling distributions
Biased and unbiased point estimates: Sampling distributions
Unit 10: Inference for categorical data: Proportions
Setting up a test for a population proportion: Inference for categorical data: Proportions
Unit 11: Inference for quantitative data: Means
Carrying out a test for a population mean: Inference for quantitative data: Means
Unit 12: Inference for categorical data: Chi-square
Unit 13: Inference for quantitative data: slopes
Unit 14: Prepare for the 2022 AP®︎ Statistics Exam
https://www.khanacademy.org/math/statistics-probability
Unit 1: Analyzing categorical data
Unit 2: Displaying and comparing quantitative data
Unit 3: Summarizing quantitative data
Unit 4: Modeling data distributions
Unit 5: Exploring bivariate numerical data
Unit 6: Study design
Unit 7: Probability
Unit 8: Counting, permutations, and combinations
Unit 9: Random variables
Unit 10: Sampling distributions
Unit 11: Confidence intervals
Unit 12: Significance tests (hypothesis testing)
Unit 13: Two-sample inference for the difference between groups
Comparing two means: Two-sample inference for the difference between groups
Unit 15: Advanced regression (inference and transforming)
Unit 16: Analysis of variance (ANOVA)
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