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References for Standardization and Normal Distributions

Curated resources to deepen your understanding of z-scores, standardization, and the normal distribution.

Wikipedia Articles

  1. Standard score - Wikipedia - Comprehensive explanation of z-scores including the formula, properties, and applications in comparing values across different distributions.

  2. Normal distribution - Wikipedia - Detailed coverage of the Gaussian distribution including its mathematical properties, parameters, and why it appears so frequently in nature and statistics.

  3. 68-95-99.7 rule - Wikipedia - Explains the Empirical Rule for normal distributions, showing what percentage of data falls within one, two, and three standard deviations of the mean.

Textbooks

  1. The Practice of Statistics by Starnes, Tabor, Yates, and Moore - W.H. Freeman (2018) - The standard AP Statistics textbook with excellent coverage of normal distributions, z-scores, and probability calculations with real-world examples.

  2. Statistics: Learning from Data by Roxy Peck and Tom Short - Cengage Learning (2018) - Clear explanations of standardization and normal curve applications with step-by-step examples ideal for high school students.

Online Resources

  1. Normal Distribution Tutorial - Khan Academy - Free video lessons walking through z-score calculations, using normal tables, and interpreting probabilities in context with practice problems.

  2. AP Statistics Course Description - College Board - Official course framework explaining exactly what students need to know about normal distributions for the AP exam.

  3. StatKey: Normal Distribution Calculator - Lock5stat.com - Interactive online tool for visualizing normal curves, calculating areas, and performing inverse normal calculations without tables.

  4. Seeing Theory: Normal Distribution - Brown University - Beautiful interactive visualizations demonstrating how the normal curve relates to data distributions and probability.

  5. The Normal Distribution and Z-Scores - Statistics by Jim - Accessible explanations with real-world examples showing how z-scores enable fair comparisons across different contexts and measurements.