Further Reading: Numerical Summaries — Center, Spread, and Shape

Books (Start Here)

Wheelan, C. (2013). Naked Statistics: Stripping the Dread from the Data. W.W. Norton & Company. Chapters 2-3 cover measures of center and spread in the same conversational tone as this textbook. Wheelan's explanation of why the mean lies about income is one of the best in popular statistics writing — it pairs perfectly with Case Study 1. He also has an excellent intuitive explanation of standard deviation that reinforces the "typical distance from the mean" interpretation. If you liked Chapter 6, you'll love these chapters.

Spiegelhalter, D. (2019). The Art of Statistics: How to Learn from Data. Basic Books. David Spiegelhalter — one of the world's most respected statisticians — devotes careful attention to summary statistics and their misuse. His treatment of how averages can mislead (especially in income and health data) is rigorous but accessible. Chapter 1 covers much of the same ground as Chapter 6 of this textbook, but with different examples drawn from UK public health and crime data. An excellent "second perspective" on the same concepts.

McGrayne, S. B. (2011). The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Fought Cancer, and Won the Nobel Prize. Yale University Press. While primarily about Bayesian statistics (which you'll encounter in Chapter 9), McGrayne's book includes fascinating historical context about how statisticians developed the tools you learned in this chapter. The evolution from simple averages to variance and standard deviation involved centuries of intellectual struggle. Reading about those struggles can make the formulas feel less arbitrary and more like hard-won insights.

Tukey, J. W. (1977). Exploratory Data Analysis. Addison-Wesley. This is the book where John Tukey introduced the box plot. It's a classic — though its style is dense and academic, quite different from modern textbooks. If you're curious about the original thinking behind the box-and-whisker plot, the five-number summary, and the 1.5 × IQR rule for outliers, Tukey's book is the primary source. Even skimming the sections on box plots and stem-and-leaf plots (which Tukey also invented) is worthwhile.

Ellenberg, J. (2014). How Not to Be Wrong: The Power of Mathematical Thinking. Penguin. Ellenberg's book includes several excellent discussions relevant to this chapter: why averages are misleading, how to think about variance and spread, and why understanding the shape of a distribution matters more than memorizing its center. His writing is witty and rigorous. The chapters on expected value and the law of averages connect directly to the mean and standard deviation concepts here.

Articles and Papers

Huff, D. (1954). How to Lie with Statistics. W.W. Norton & Company. The classic (and still highly readable) guide to statistical deception. Huff's chapter on "The Well-Chosen Average" — which explores exactly the mean vs. median confusion from Case Study 1 — is required reading for any statistics student. The book is short (144 pages), entertaining, and shockingly relevant 70+ years after publication. If you read one supplementary source for this chapter, make it this one.

Mishel, L., & Kandra, J. (2021). "CEO Pay Has Skyrocketed 1,322% Since 1978." Economic Policy Institute Report. This report provides the actual data behind the CEO-pay-vs.-worker-pay analysis in Case Study 1. It clearly shows how mean vs. median CEO compensation tell different stories and includes the historical trend data. Freely available at epi.org. A concrete application of everything you learned about skewed distributions and resistant measures.

Anscombe, F. J. (1973). "Graphs in Statistical Analysis." The American Statistician, 27(1), 17-21. Mentioned in Chapter 5's further reading as well, but worth revisiting now. Anscombe's four datasets have identical means and standard deviations — proving that summary statistics alone can be deeply misleading without accompanying visualizations. After learning the formulas in Chapter 6, seeing Anscombe's Quartet drives home the lesson that numbers and pictures must work together.

Matejka, J., & Fitzmaurice, G. (2017). "Same Stats, Different Graphs." CHI Conference Proceedings. The modern extension of Anscombe's work — the "Datasaurus Dozen." Thirteen datasets with identical summary statistics (mean, standard deviation, and correlation) that look completely different when graphed, including one shaped like a dinosaur. A vivid demonstration that summary statistics, no matter how carefully calculated, cannot replace looking at your data. Search "Datasaurus" for the visualizations.

Videos

StatQuest with Josh Starmer — "Standard Deviation vs Standard Error" (YouTube, ~12 min) Starmer clearly distinguishes standard deviation (which you learned in this chapter) from standard error (which you'll learn in Chapter 11). Watching this video now gives you a preview of where standard deviation is heading — and prevents a common confusion that trips up many statistics students later. Starmer's "quest" format breaks complex ideas into digestible steps.

StatQuest with Josh Starmer — "The Normal Distribution, Clearly Explained" (YouTube, ~5 min) A concise animated explanation of the bell curve and the Empirical Rule. This video reinforces Section 6.7 and previews Chapter 10's deeper treatment of the normal distribution. Great for visual learners who want to see the 68-95-99.7 pattern animated.

3Blue1Brown — "Why Do We Divide by n-1?" (YouTube, ~18 min) Grant Sanderson provides a beautiful geometric/visual explanation of why the sample variance formula uses $n-1$ instead of $n$. It's more mathematical than the intuitive explanation in Section 6.5, but Sanderson's animations make the concept genuinely intuitive. If the $n-1$ explanation in this chapter left you wanting more, this video delivers.

Vox — "Why the Median Is Usually Better Than the Average" (YouTube, ~8 min) A well-produced explainer video that covers the mean-vs-median distinction using income data — essentially a video version of Case Study 1. Useful for reinforcing the concepts and seeing the same ideas presented from a journalism perspective.

Khan Academy — "Box and Whisker Plots" (khanacademy.org, ~12 min) Sal Khan walks through box plot construction step by step, with animated examples. If you want extra practice reading and creating box plots before tackling the exercises, this is an excellent resource. Free, with practice problems embedded.

Interactive and Online Resources

Seeing Theory — "Basic Probability" and "Descriptive Statistics" (seeing-theory.brown.edu) This beautiful interactive website from Brown University includes modules on measures of center, measures of spread, and the Empirical Rule. You can drag data points around and watch the mean, median, and standard deviation update in real time. Spending 15-20 minutes with the interactive tools builds intuition faster than static examples.

GeoGebra Box Plot Applet (geogebra.org — search "box plot") Several interactive box plot tools let you enter your own data and see the five-number summary, fences, and outliers calculated automatically. Try entering skewed datasets and symmetric datasets to see how the box plots differ. Also try adding and removing outliers to see their effect on the mean vs. median.

FRED (Federal Reserve Economic Data) (fred.stlouisfed.org) The Federal Reserve's free data portal includes time series of median and mean household income, wealth distribution data, and economic indicators. Search for "Real Median Household Income" and compare it to "Real Mean Household Income" — you'll see the divergence discussed in Case Study 1 playing out across decades. An excellent source for the progressive project if you're interested in economic data.

Our World in Data (ourworldindata.org) This Oxford-based project provides free data and visualizations on global health, poverty, education, and environment. Their income inequality pages include excellent box plots and distribution comparisons across countries. Relevant to both Case Study 1 and the broader themes of this chapter.

Python Graph Gallery — Box Plots (python-graph-gallery.com/boxplot/) A collection of Python code examples for creating box plots using matplotlib and seaborn. Includes side-by-side box plots, grouped box plots, violin plots (a variation you'll see in later chapters), and customization options. Invaluable as you build your Python visualization skills beyond the basics covered in Section 6.6.

Podcasts

Cautionary Tales with Tim Harford — "The Deadly Bullet Graph" (~30 min) Tim Harford (author of The Data Detective) tells the story of how poor statistical communication — including misunderstandings about averages and spread — led to catastrophic decisions. While not specifically about Chapter 6 concepts, it reinforces why getting summary statistics right matters in high-stakes contexts.

Data Skeptic — "Descriptive Statistics" (dataskeptic.com) A 15-minute episode covering means, medians, standard deviations, and when each is appropriate. Clear, concise, and pitched at the right level for introductory students. A good audio companion to this chapter.

Looking Ahead

The concepts in this chapter are foundations for everything that follows:

  • Chapter 7 (Data Wrangling): You'll use summary statistics to diagnose data quality issues — a mean that doesn't make sense, a standard deviation that's suspiciously large, or outliers that turn out to be data entry errors
  • Chapter 8 (Probability): The variation you measured in this chapter connects directly to probabilistic thinking — the more spread out your data, the more uncertain you are about any given observation
  • Chapter 10 (Normal Distribution): The Empirical Rule evolves into the full normal distribution model, and z-scores become your primary tool for calculating exact probabilities
  • Chapter 11 (Central Limit Theorem): Standard deviation transforms into "standard error" — the standard deviation of a sampling distribution — bridging descriptive and inferential statistics
  • Chapter 12 (Confidence Intervals): Standard deviation and z-scores are the building blocks of confidence intervals
  • Chapter 13 (Hypothesis Testing): Z-scores become test statistics, and the "how unusual is this value?" reasoning from the Empirical Rule becomes the logic of p-values
  • Chapter 22 (Regression): Variance decomposes into "explained" and "unexplained" components, connecting directly to $r^2$