The Missing 11th of the Month

Summary

The Missing 11th of the Month Source xkcd. Image licensed under CC-BY-NC. On November 28th, 2012, Randall Munroe published an xkcd comic that was a calendar in which the size of each date was proportional to how often each date is referenced by its ordinal name (e.g. "October 14th") in the Google Ngrams database since 2000. Most of the large days are pretty much what you would expect: July 4th, December 25th, the 1st of every month, the last day of most months, and of course a September 11th that shoves its neighbors into the margins. There are not many days that seem to be smaller than the typical size. February 29th is a tiny speck, for instance. But if you stare at the comic long enough, you may get the impression that the 11th of most months is unusually small. The title text of the comic concurs, reading "In months other than September, the 11th is mentioned substantially less often than any other date. It's been that way since long before 9/11 and I have no idea why." After digging into the raw data, I believe I have figured out why. First I confirmed that the 11th is actually interesting. There are 31 days and one of them has to be smallest. Maybe the 11th isn't an outlier; it's just on the smaller end and our eyes are picking up on a pattern that doesn't exist. To confirm this is real, I compared actual numbers, not text size. The Ngrams database returns the total number times a phrase is mentioned in a given year normalized by the total number of books published that year. The database only goes up to the year 2008, so it is presumably unchanged from when Randall queried it in 2012. I retrieved the count for each day for the year (January 1st, January 2nd etc.) and took the median over the months for each day (median of January 1st, February 1st, etc.) for each year. This summarizes how often the 11th and the other 30 days of the month appear in a given year. Using the median prevents outlier days like July 4th from dragging up the average for its correspon...