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References for Numerical Summaries

Curated resources to deepen your understanding of measures of center, spread, the five-number summary, boxplots, and standard deviation.

Wikipedia Articles

  1. Mean - Wikipedia - Comprehensive coverage of the arithmetic mean and related concepts. Explains the mean as a balance point and discusses when the mean is an appropriate measure of center.

  2. Standard deviation - Wikipedia - Detailed explanation of standard deviation including formulas, interpretation, and relationship to variance. Covers both population and sample calculations with clear examples.

  3. Box plot - Wikipedia - Explains boxplot construction including the five-number summary, whiskers, and outlier detection using the 1.5 IQR rule. Includes variations like notched boxplots and violin plots.

Textbooks

  1. The Practice of Statistics by Daren S. Starnes, Josh Tabor, and Dan Yates - W.H. Freeman (2018) - Chapters 1-2 provide thorough coverage of numerical summaries including mean, median, quartiles, standard deviation, and boxplots. The emphasis on interpretation over calculation aligns well with AP exam expectations.

  2. Introduction to the Practice of Statistics by David S. Moore, George P. McCabe, and Bruce A. Craig - W.H. Freeman (2017) - College-level text with clear explanations of descriptive statistics. Excellent treatment of when to use resistant versus non-resistant measures based on distribution shape.

Online Resources

  1. Khan Academy: Summarizing Quantitative Data - Khan Academy - Video series covering mean, median, mode, range, IQR, variance, and standard deviation. Includes practice problems on calculating and interpreting all measures.

  2. GeoGebra Classroom: Boxplot Tool - GeoGebra - Free interactive tool for creating boxplots from entered data. Shows the five-number summary and allows comparison of multiple groups side by side.

  3. Stat Trek: Measures of Central Tendency - Stat Trek - Clear explanations of mean, median, and mode with worked examples. Includes discussion of when each measure is most appropriate.

  4. PhET Interactive Simulations: Mean and Standard Deviation - University of Colorado Boulder - Interactive simulation where students can explore how adding or moving data points affects mean and standard deviation in real time.

  5. Art of Problem Solving: Statistics - AoPS - Problem-solving focused approach to descriptive statistics. Challenging practice problems that go beyond routine calculation to test conceptual understanding.