Back to math class for the Globe

We’re all familiar with the warning to keep matches out of the hands of children. The same should often be said with respect to statistics and reporters.

Today’s exhibit: The front-page story by Beth Teitell in the Boston Globe telling us that, 55 years after Marilyn Monroe made the idea famous in The Seven Year Itch, marriages continue to fall apart around the seven-year mark. The basis for Teitell’s story? Census data released this year showing that first marriages that ended in divorce lasted a median of eight years, with couples separating after median of about seven years.

From there, the piece proceeds in cookie-cutter fashion: She finds a few of the requisite anecdotal examples to support the claim – couples that split up after seven years (and somewhat inexplicably agreed to share their story with us all). Then a few “experts” weigh in with various evidence-free “explanations” for why the Big Split tends to happen at the seven-year mark.

What’s wrong with all this? There is no basis for concluding, based on the Census figures provided in the story, that couples tend to divorce after seven years. The median is the point above and below which half of all values lie. It does not denote the number with the greatest frequency in a set of values. That is the mode.

Imagine there were a total of 20 divorces in the U.S. in a given year, and that the duration of these marriages, in years, was as follows:

1, 1, 2, 3, 3, 3, 3, 3, 5, 6, 8, 10, 10, 11, 12, 13, 14, 14, 15, 32

The median length of marriages ending in divorce is 7 years, since 10 of the couples divorced after less than 7 years of marriage and 10 split up after more than 7 years. None of the couples actually divorced after 7 years. The most common point at which couples divorced in this example clearly is after 3 years, the point at which fully one-quarter of all divorces occurred.

Based on the Census figure used in the story, we simply have no idea what the most frequent duration of marriage is among those unions that end in divorce. But that evidently wasn’t enough to get in the way of a good story that, with its Marilyn Monroe tie-in, had legs.

                                                                                                                                                                                –Michael Jonas