## Kindergarten Math

Alex and Eli started kindergarten on Tuesday.

At a “Meet the Teacher” event last week, we were told that this is the most kindergarten classes they’ve had at the school. “We had to add another class this year, so we now have eight,” one of the teachers said.

“How many students are in each class?” I asked.

“Twenty-one,” she said, “so it’s really good that we added that eighth class — or else there’d be, like, 26 students in each class!”

I was too polite to tell her that 8 × 21 ≠ 7 × 26.

Today, we had a parent-teacher conference. On the bulletin board in her class was the following chart with student names:

Click Image to Enlarge

There are 19 students in the class, and all of them have a first name that that begins with a letter in the first half of the alphabet. There are 3 A’s, 1 B, 3 C’s, 1 D, 2 E’s, 1 I, 3 K’s, 3 L’s, and 1 M.

I mentioned this to the teacher. “I know!” she said. “Isn’t that an amazing distribution!”

Well, yeah, I thought. It’s quite amazing, in fact.

If you assume that names are evenly distributed across the alphabet, the probability that all 19 students would have a first name in the first half of the alphabet is an astounding (1/2)19 = 0.00000002%.

But of course, names are not evenly distributed across the alphabet. I don’t know how they’re distributed, but the first letters of English words are distributed as follows:

Click Image to Enlarge

That means that 52.005% of all English words start with a letter in the first half of the alphabet. If you assume that names follow the same distribution, then the probability doubles to 0.00000004%.

Yup. Still pretty low.

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• 1. xander  |  September 7, 2012 at 1:05 am

On the other hand, what is the probability that no class in [Your State] / the US / the world has such a distribution? Someone has to be in the class with only A through Ms. 😉

• 2. Joshua Zucker  |  September 7, 2012 at 2:14 am

First letters of English words is probably not a very good approximation. One of the first things I noticed from the list on the board there was that there were no “J” names — amazing! Not a single John, Jennifer, Julie, … maybe I’m living in the wrong decade, though. http://www.babycenter.com/0_100-most-popular-baby-names-of-2007_3637303.bc tells me that the girl J names are really not at all popular in this cohort, but that there are a lot of Jacobs, Jacksons, and Jacks, and … Jayden?!

Also I’m impressed that Jordan has lasted so long as being a name for both girls and boys. It seems to me like names start being used for girls and that quickly takes them out of the running for boys names.

• 3. venneblock  |  September 7, 2012 at 10:54 am

Yep, I knew it wasn’t necessarily a good assumption… but in the absence of other data, I thought it was a reasonable approach. Perhaps not, though.

I was able to find an analysys of letter frequency in account names, and it seems that the analysis used the first letter of the account holder’s first name. It’s only based on a sample size of 500K, but I’d think it would give a reasonable approximation to the larger population. And as you said, it differs quite a bit from the distribution of first letters in English words.
http://etbe.coker.com.au/2008/06/20/letter-frequency-in-account-names/

For a comparison of the first letters from this account analysis to English words, see https://mathjokes4mathyfolks.files.wordpress.com/2012/09/firstletterfrequency1.png.

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