What is Charles Wheelan’s Naked Statistics about? What statistics does Wheelan explore in the book?

Naked Statistics puts the math behind statistics into digestible terms and explains statistics concepts with relatable, relevant, and even humorous examples. Readers also benefit from additional socio-political insight from the book, as Wheelan uses real-world anecdotes to explore how statistics can inform collective decision-making.

Below is a brief overview of the key themes and concepts from Wheelan’s Naked Statistics.

## Naked Statistics: Stripping the Dread from the Data

Wheelan opens Naked Statistics with the admission that he sometimes struggled to see the relevance of what he was learning as a math student. Therefore, he puts the relevance of statistics front and center in the book, building his discussion of each statistics concept around why we should know about it. Better yet, Wheelan proves that statistics don’t need to be intimidating by putting the math behind statistics into digestible terms and explaining concepts with relatable, relevant, and even humorous examples.

This guide largely focuses on two main themes in Charles Wheelan’s Naked Statistics. First, we cover what many common statistics mean, how to interpret them, and why they matter. Like Wheelan, we use real and fictional examples to add context to each statistic covered. Second, we examine Wheelan’s discussion of the consequences of bias and the misapplication and misinterpretation of statistics to make the case that everyone should develop basic statistical literacy.

### Statistics Organize Data

We rely on data to make sense of the world, but without statistics, datasets would be largely useless. Imagine asking a car salesperson what kind of mileage a car gets, only to get a 100-page spreadsheet of the individual miles that car has driven and how much gas it used each mile! While the spreadsheet may be comprehensive, it’s also pretty useless if you were hoping for a quick answer. With statistics, we can take unwieldy datasets and transform them into meaningful and actionable values, like average miles per gallon.

Statistics that summarize datasets are called descriptive statistics. Two of the most familiar and commonly used descriptive statistics are the mean (the average) and the median (the middle number when you put all of your data in numerical order). The mean and median are called measures of central tendency, and while they both tell us about the “middle” of a dataset, Wheelan explains that they can convey very different messages. With a basic understanding of statistics, we can learn when to use one over the other and spot when someone might be reporting the mean instead of the median (or vice versa) to further an agenda.

Say the beach authorities at a fictional beach were collecting data on the number of jellyfish stings swimmers suffered each week throughout the summer. The data might look something like this:

(Shortform note: In this example, the dataset is naturally ordered, so we don’t need to order it to determine the median.)

The mean number of jellyfish stings is 42. The median number of stings is zero. Beach authorities could either say:

A) “Visit our beach! The mean number of weekly stings/500 swimmers throughout the summer is only 42!”

or

B) “Visit our beach! The median number of weekly stings throughout the summer is zero!”

Neither of these statements is incorrect, but they convey a different message to prospective swimmers. The beach authorities are sure to advertise option B over option A because option B makes the beach look more attractive. As astute statistics students, we should question which measure of central tendency best captures the “story” of the dataset and be aware that no single statistic can fully convey real-world complexity.

### Statistics Reveal and Describe Relationships

Descriptive statistics can also illuminate and describe relationships between variables in a dataset. As Wheelan explains, analyzing the correlation between two variables can tell us whether a change in one variable corresponds to a change in the other. For example, a nursery owner might find a positive correlation between the hours of sunlight her mums get and the number of blooms on each plant. The number of flowers on each plant increases predictably with sunshine. In contrast, she might find a negative correlation between the number of ladybugs on her plants and the number of aphids. As the number of ladybugs (which eat aphids) increases, the number of aphids decreases.

The correlation coefficient communicates the strength of the relationship between two variables, with a coefficient of one meaning a “perfect correlation” and a coefficient of zero meaning “no meaningful relationship.” We can use the value of the correlation coefficient to help guide both our research and our actions. For example, say researchers investigating lead poisoning found a correlation coefficient of 0.8 between the amount of city water children drank and lead levels in their blood. This large positive correlation can’t prove that city water is causing lead poisoning. But, these findings would warrant investigating the city’s water quality and might lead parents to purchase bottled water.

Another statistics technique, regression analysis, goes beyond describing the relationship between two variables and allows us to make mathematical predictions based on those relationships. For example, the nursery owner above could generate an equation with regression analysis to predict how many flowers her plants would have based on the amount of sunlight she gave them.

### Statistics Help Answer Complicated Questions

Probability is one way statistics can help us make more informed decisions. It allows us to manage uncertainty, calculate risks, and put possible outcomes in perspective. Wheelan explains that understanding probability can be especially relevant to our daily lives because we make decisions based on our perception of probability all the time. However, our perception of likely outcomes is often mathematically irrational. For example, the probability of getting in a car accident while driving to a beach is far higher than the probability of being attacked by a shark there, but we often—irrationally—fear the shark risk more.

People often use probability to assess risk when making financial decisions. Wheelan explains that a statistic called the “expected value” can help us determine whether we want to take a financial risk when we know the probability of each possible outcome and its respective payoff. Real-estate developers, for instance, can use this tool to make sure that their multiple investments are likely to make money as a whole. Even if one property loses money or underperforms in a given year, as long as the expected value of their portfolio is profitable overall, they are likely to make money.

In addition to helping us make more informed decisions, statistics can offer insight into questions we couldn’t possibly design an experiment to answer. For example, say we wanted to know whether exposure to a certain chemical (we’ll call it chemical X) corresponds to higher rates of cancer. Ethics precludes purposefully exposing people to chemical X in a laboratory setting for the sake of science. Additionally, so many other variables impact a person’s personal cancer risk that we can’t possibly know if chemical X was the sole cause of anyone’s cancer diagnosis. Without statistics, complex but important questions like this would remain unanswered.

To answer the question of whether chemical X is associated with higher rates of cancer, researchers could collect a large dataset including people who were and were not exposed to chemical X and record their rates of cancer diagnoses. Then the researchers could use regression analysis to determine the association between exposure to chemical X and a cancer diagnosis, independent of other factors such as smoking, exercise, family history, and so on. Statistics can even tell us what percent of a person’s overall cancer risk is mathematically associated with exposure to chemical X rather than other factors.

As Wheelan explains, the ability to mathematically separate individual variables (like exposure to a particular chemical) in the complexity of the real world makes statistical analysis an invaluable part of medical and social sciences research.

### Learning Statistics Is Empowering

Learning statistics is an exercise in self-empowerment. Wheelan explains that thanks to modern society’s affinity for and reliance on technology, we’re constantly surrounded and impacted by data. This abundance of data is a blessing in that it gives researchers a chance to study society’s most pressing issues, for example, using student outcomes to highlight racial and social inequities in our education system. But, the amount of data we’re bombarded with every day through targeted marketing, political campaigns, and social media can also be a challenge when we don’t know how to gauge its reliability. Studying statistics can give us a better sense of how much trust we should put in different sources of information and can help us interpret published statistics correctly.

Studying statistics also makes us less susceptible to being purposefully misled. Unfortunately, Wheelan explains that the purposeful misuse of statistics is more common than we may think. While the statistics values themselves can’t lie, the statistical tests that people choose to use, the data they choose to calculate statistics with, and the choice to include or not include specific statistics from datasets can construct various versions of “the truth.” For example, consider the following statements based on the same hypothetical dataset:

• Vote for Mark Smith! His tax cuts have saved the people in this town an average of \$1,000 per year!
• Don’t vote for Mark Smith! His “tax cuts” have saved the wealthiest 1% of town residents tons of money and have saved low-income residents almost nothing!

Neither of these statements is a lie. Instead, different uses of data and statistics construct versions of the truth that best suit differing perspectives. While we can’t expect ourselves to dive into the underlying data for every statistic we read or hear, Wheelan explains that we can better spot incomplete or misleading information with a basic understanding of statistics.

Charles Wheelan: Naked Statistics (Overview)

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#### Like what you just read? Read the rest of the world's best book summary and analysis of Charles Wheelan's "Naked Statistics" at Shortform .

Here's what you'll find in our full Naked Statistics summary :

• An explanation and breakdown of statistics into digestible terms
• How statistics can inform collective decision-making
• Why learning statistics is an exercise in self-empowerment

#### Darya Sinusoid

Darya’s love for reading started with fantasy novels (The LOTR trilogy is still her all-time-favorite). Growing up, however, she found herself transitioning to non-fiction, psychological, and self-help books. She has a degree in Psychology and a deep passion for the subject. She likes reading research-informed books that distill the workings of the human brain/mind/consciousness and thinking of ways to apply the insights to her own life. Some of her favorites include Thinking, Fast and Slow, How We Decide, and The Wisdom of the Enneagram.