Blog by Sean Trott: “…The goal of this post is to distill what I take to be the most important, immediately applicable, and generalizable insights from these classes. That means that readers should be able to apply those insights without a background in math or knowing how to, say, build a linear model in R. In that way, it’ll be similar to my previous post about “useful cognitive lenses to see through”, but with a greater focus on evaluating claims specifically.
Lesson #1: Consider the whole distribution, not just the central tendency.
If you spend much time reading news articles or social media posts, the odds are good you’ll encounter some descriptive statistics: numbers summarizing or describing a distribution (a set of numbers or values in a dataset). One of the most commonly used descriptive statistics is the arithmetic mean: the sum of every value in a distribution, divided by the number of values overall. The arithmetic mean is a measure of “central tendency”, which just means it’s a way to characterize the typical or expected value in that distribution.
The arithmetic mean is a really useful measure. But as many readers might already know, it’s not perfect. It’s strongly affected by outliers—values that are really different from the rest of the distribution—and things like the skew of a distribution (see the image below for examples of skewed distribution).
In particular, the mean is pulled in the direction of outliers or distribution skew. That’s the logic behind the joke about the average salary of people at a bar jumping up as soon as a billionaire walks in. It’s also why other measures of central tendency, such as the median, are often presented alongside (or instead of) the mean—especially for distributions that happen to be very skewed, such as income or wealth.
It’s not that one of these measures is more “correct”. As Stephen Jay Gould wrote in his article The Median Is Not the Message, they’re just different perspectives on the same distribution:
A politician in power might say with pride, “The mean income of our citizens is $15,000 per year.” The leader of the opposition might retort, “But half our citizens make less than $10,000 per year.” Both are right, but neither cites a statistic with impassive objectivity. The first invokes a mean, the second a median. (Means are higher than medians in such cases because one millionaire may outweigh hundreds of poor people in setting a mean, but can balance only one mendicant in calculating a median.)..(More)”