Intertops has a prop bet on the value of the tenths digit of the Dow Jones Industrial Average at market close. It’s certainly not a very attractive prop bet, with each selection 0 through 9 returning only 8-1. But it got me wondering — do the values 0 through 9 appear approximately equally often as the tenths digit of the Dow close?
As you may or may not know, the Dow Jones Industrial Average is a weighted average of 30 stocks. The 30 stocks that comprise the Dow are changed every once in a while, but have not changed since June 8, 2009. Looking at the daily close of the Dow beginning with that date (you can use Yahoo! Finance if you are interested in these data), we have the following:
One would expect that each digit should have appeared approximately 29 times over the course of the 290 closes starting June 8, 2009. But the 9 has appeared 41 times! Now, I have no idea what factors may influence the value of the tenths digit, I am simply interested if the data suggest that some values appear more often than others. To do this, a Chi-Square statistical test can be run on the data; OpenOffice.org Calc and other spreadsheets can do this for you.
The resulting chi-square statistic has a probability of 0.09, meaning that if you randomly picked values from 0 through 9 290 times, the probability that you would get a distribution similar to the one shown in the table above is only 9%. That’s fairly rare, but not overly so.
But, if you were going to make this prop bet, pick the 9. 🙂