The author observes that students who find statistics confusing often discuss statistical concepts comfortably in everyday contexts like batting averages. The NFL passer rating exemplifies a useful but imperfect descriptive statistic: Comparing Jay Cutler’s playoff rating of 31.8 to Aaron Rodgers’s 55.4 efficiently explains why the Chicago Bears lost to the Green Bay Packers in 2011. Similarly, the Gini index measures income inequality on a scale from zero to one, enabling comparisons across countries. Sweden’s index of .23 indicates greater equality than that of the United States at .45 or South Africa at .65. Statistics process data to transform raw information into meaningful insights.

Statistics serve four main functions. First, description and comparison summarize complex information using tools like averages. Second, inference uses samples to make informed conjectures about larger populations, as with political polling or studies of sexual behavior. Third, assessing risk and probability allows casinos and insurance companies to manage uncertainty. For instance, the firm Caveon Test Security uses probability to detect cheating by identifying statistically unlikely patterns of identical wrong answers on exams. Finally, identifying important relationships through statistical detective work allows researchers to isolate associations while controlling for confounding factors. For example, Princeton economist Alan Krueger’s terrorism research found that terrorists tend to be well educated and from middle- or high-income families, contradicting common assumptions. His data also showed more terrorism in countries with greater political repression. Krueger hypothesizes that because terrorists are motivated by political goals, the educated and affluent have the strongest incentives to force societal change.

The author acknowledges that statistical analysis rarely reveals absolute truth and that honest people can disagree about interpretations. Former Secretary of Defense Donald Rumsfeld’s aphorism about working with available resources applies equally to research with imperfect data. Statistics can be deliberately misused or lead to inadvertent errors, making it essential to recognize both legitimate findings and manipulation.

Wheeler opens by asking two questions related by the answers’ use of statistics. First, what is the financial health of the US middle class? And second, who is the greatest baseball player ever? Descriptive statistics summarize large data sets by finding different kinds of middle points. Derek Jeter’s career batting average of .313 encapsulates 17 seasons of performance. In contrast, using per capita income (another kind of average) to measure middle-class well-being misleads because this information is not adjusted for inflation and can be skewed by extreme wealth.

Two fundamental measures of central tendency, or the middle, are the mean and median. The mean is the average of a set of numbers, calculated by adding up the values and dividing by the number of separate values in the set. The mean is sensitive to outliers. For example, if Microsoft founder Bill Gates enters a bar where 10 patrons each earn $35,000 dollars annually, his billion-dollar income raises the patrons’ mean income to $91 million. In contrast, the median is derived by arranging a set of values in ascending order and finding the middle one. In the same bar example, even with Bill Gates in the room, the patrons’ median income remains $35,000 (the middle of the set of 11 numbers). Even if Warren Buffett joins them, the median still remains $35,000 (the middle of the set of 12 numbers).

In a printer quality comparison, one company’s products are seemingly vastly inferior: They have a mean of 9.1 defects versus a competitor’s 2.8. But the median reveals a different story. A frequency distribution shows that the first company actually has a lemon problem—most printers work well, but a few have numerous defects that inflate the mean.

Standard deviation measures dispersion around the mean, or how far most pieces of data will be from the average. For normally distributed data, 68.2 percent of observations fall within one standard deviation of the mean, and 95.4 percent within two. This property makes the normal distribution—which readers may know as the bell curve—foundational to statistics.

Percentages require careful interpretation. Wheeler poses a quick math problem to readers: If a dress is originally priced at $100, then marked down 25%, and then marked up 25%, how much does it cost? The answer is counter-intuitive: The dress now costs $93.75, not $100 (because the markup is calculating 25% of $75). In a real-world example that illustrates a similar slipperiness with percentages, Illinois’s income tax increase from 3% to 5% can be correctly described by proponents as a two-percentage-point increase and by opponents a 67% increase.

The chapter ends by returning to the questions posed at its beginning. To evaluate the greatest baseball player, Steve Moyer, president of Baseball Info Solutions, suggests using mean calculations: on-base percentage, slugging percentage, and at bats. These statistics point to Babe Ruth as the greatest player due to his unique ability to both hit and pitch. In contrast, economists Jeff Grogger and Alan Krueger recommend examining median wages, adjusted for inflation, to assess middle-class economic health. A graph of 1979 to 2011 shows that the median wage stagnated, while the 90th percentile grew significantly.

The chapter explores how technically accurate statistics can mislead. Precision differs from accuracy. Precision reflects mathematical exactitude, while accuracy measures consistency with truth and fact. For instance, Senator Joseph McCarthy’s 1950 claim about possessing a list of 205 communists in the State Department was precise, in that he named a specific number, but false, in that he had no such names. The author’s golf range finder provided precise measurements but because it was set to meters instead of yards and sometimes aimed at the wrong targets, this precise information was useless. Finally, Wall Street risk models before the 2008 crisis were precise, but built on flawed assumptions, making their conclusions harmful.

Ambiguity about what is being measured can create contradictory but simultaneously true statements. For example, data from The Economist show US manufacturing output rising while employment falls. This is because the units of analysis differ: With greater automation, productivity can increase while fewer workers are being hired. Likewise, examining the quality of schools as a whole versus the preparedness of students individually can yield opposite conclusions. Similarly, global inequality appears to have gotten worse over time when countries are the unit of analysis. However, when people are the unit, we can see that global inequality has actually been falling, because a high proportion of the world’s poor live in fast-growing nations like China and India.

The mean and median can be selectively cited to support opposing narratives. The George W. Bush administration promoted tax cuts by citing a mean reduction exceeding $1,000 per household. But this average hid the fact that the median for most households was actually under $100—a huge tax break for a small number of very rich people skewed the mean. Conversely, the median can obscure important information. Evolutionary biologist Stephen Jay Gould survived for 20 years after being diagnosed with a cancer with a median survival time of eight months. The median does not account for the extent and frequency of occurrence of outliers.

Inflation adjustment is crucial for comparisons of money across time. Hollywood reports box office using nominal dollars, without inflation adjustment, making recent films like Avatar (2009) appear more successful than older ones. When adjusted for inflation, Gone with the Wind (1939) tops the list, while Avatar falls to 14th. The US minimum wage’s nominal value has risen seemingly dramatically, but in reality, its real purchasing power has declined.

Manipulating timeframes also alters narratives. The author’s professor used identical defense spending data to praise either President Ronald Reagan or President Jimmy Carter depending on the political leanings of his audience; his graph of defense spending over the years could be zoomed in to show Reagan as increasing spending, or zoomed out to show Carter as the originator of a defense boom. Percentages can exaggerate when calculated from small bases. A seemingly enormous annual 527% tax increase for a Tuberculosis Sanitarium District actually cost homeowners less than a sandwich because it was increasing an initial value of $1.15 to $6.70.

Measuring the wrong thing creates perverse incentives. For example, using test scores alone to evaluate schools created not a better educational system, but a strong push for administrators to cheat the tests. In Houston, Texas, schools under Superintendent Rod Paige manipulated dropout statistics by reclassifying departing students and kept weak students from taking benchmark exams to inflate averages. Other testing scandals involved teachers supplying correct answers to students or correcting tests themselves before submitting them. Similarly, New York’s cardiologist scorecards about surgery outcomes led doctors to simply avoid operating on the sickest patients to protect their mortality statistics.

Measuring the wrong thing can also mislead about cause and effect. Chicago newspapers rank selective enrollment schools as best based on test scores, but admission to these schools requires high scores from applicants. This means that the kids who get in are likely to continue testing well. Praising schools for this is the logical equivalent of praising a basketball team for producing tall students.

Wheelan ends the chapter by critiquing the U.S. News & World Report college rankings, which use arbitrary weighting and focus on inputs rather than outcomes. Critics like Michael McPherson note the rankings lack genuine precision. Despite these criticisms, Bard College president Leon Botstein acknowledges people crave simple answers—this is why rankings will never go away. The chapter concludes that statistical malfeasance stems from poor judgment (accuracy) rather than mathematical errors (precision).