Don’t Be Fooled by the Mean (or How to Avoid Absurd Statistical Claims in Your PR and Market Research Surveys)
Even smart people get tripped up by simple statistics, as this statement from a recent New Yorker article demonstrates: A hundred years ago, most Americans died in their mid-fifties. This was written by a seasoned journalist, for a publication that has good editors. Most likely this claim was “verified” by a fact checker, as well.
But, obviously, it is not true. Just imagine what this would look like. Millions of people going along, living their lives, and then they reach age 54 or 55 and over half of them suddenly die.
It seems the author of this sentence dug up a statistic about average life expectancy, and mistakenly interpreted it to mean “most.”
It made me curious to see the statistics myself. I downloaded the 1923 mortality tables from the U.S. Census Bureau. The average U.S. life expectancy in that year was 56.1 for men and 58.5 for women. But of course the mortality tables show a much richer (and more correct) story:
Of all the people who died that year (and despite the average life expectancy) only one in nine (11%) were in their 50s. Looking up the number of people who were alive that year from a different data table, shows that for every 1 person in their 50s who died, there were 99 others who lived. And take a look at the tables again. Compared to the number who died in their 50s, twice as many were children under the age of five. Three times as many died at much older ages beyond 59. No, most Americans were not dying in their mid-fifties. Not even close.
Life expectancy numbers are tricky. Even smart people get tripped up by them. And they are a good reminder that “average” or “mean” rarely means “most.” To understand the mean, you need to look at the underlying data from which the mean is calculated.
That’s one reason we tell our clients we will review their public release statements based on data from our research for free. It ensures that any claims they make are an accurate and true interpretation of the data.
—Joe Hopper, Ph.D.