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A Timely Math Lesson

How small statistical samples can lead you in the wrong direction.

by Hannah Mitchell
January 16, 2025
A Timely Math Lesson

Picking out an extreme statistical example in meetings with customers can be misleading.

Credit:

Pexels/Lukas

3 min to read


Math was always my weakest subject in school, and I studiously avoided the more advanced courses as much as possible. Though I did take statistics in college, I remember nothing from the class, at least not consciously.

My career as a writer and editor has ironically forced me to get better at my everyday use of numbers to make sense of data and communicate it to readers. And in my current reading of a book by Nobel Prize-winning psychologist and researcher Daniel Kahneman, who died last March, I’m learning more that’s helping me make better sense of automotive industry statistics.

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Thinking, Fast and Slow,” published in 2011, is jam-packed with insights on how the human mind works, from decision-making to how we form impressions and interpret our world. 

One chapter in particular helped me gain new insight that could come in handy in the F&I office. It digs into how small research samples can be misleading. An example is a high rate of new kidney cancer cases in sparsely populated U.S. counties. Kahneman explains that, “extreme outcomes (both high and low) are more likely to be found in small than in large samples.”

So when I saw a recent LendingTree study about car thefts that pointed out a dramatic spike in Vermont between 2020 and 2022, I left the example out of my news item on the report. That’s because Vermont is the second smallest state by population, with far fewer residents than many larger U.S. cities. It’s an example of an extreme outcome.

What does this have to do with F&I? I share it because F&I managers need examples of the latest research to demonstrate their expertise and make relevant points to customers. Picking out extreme examples such as the Vermont theft rate could be misleading, painting a picture of car thieves run amuck on every street in the largely rural state, whereas the theft rate per 100,000 residents in 2023 would offer much more reality. The District of Columbia leads that list at about 1,150, according to LendingTree data.

Or as Kahneman further explained in the kidney cancer example:

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“The incidence of cancer is not truly lower or higher than normal in a county with a small population, it just appears to be so in a particular year because of an accident of sampling. If we repeat the analysis next year, we will observe the same general pattern of extreme results in the small samples, but the counties where cancer was common last year will not necessarily have a high incidence this year.”

Even though I hated math growing up, I did appreciate the rare math teacher who was good at breaking it down into bite-sized steps that even I could absorb and understand. Kahneman was just one of those teachers that I happened upon. Hopefully his analysis will help you, too.

Hannah Mitchell is executive editor of F&I and Showroom.A former daily newspaper journalist, she honed her craft covering politics, business and more for publications that included the Charlotte Observer and the Orange County (Calif.) Business Journal. She holds a master’s degree in journalism from Columbia University, and her first car was a hand-me-down Chevrolet Nova.

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