Archive for January, 2014

Fun trivia on how many people it takes before chances are good that some or all share birthdays

Birthdays are in the news this month as the last of the Baby Boomers hit age 50—most notably Michelle Obama, but also my youngest sibling—brother Paul.  A little game I’ve played with my larger statistics classes is to poll them for their birthday—month and day (one mustn’t dare to ask for the year).  It turns out that with 23 people coming together at random the odds tilt in favor of at least two sharing this special date.  Somehow that just does not seem likely but all one needs to do for working this out is calculate the probability of all having different birthdays, and then subtract the answer from 1.

By the way, it takes 88 people to achieve a good chance of 3 sharing a birthday.

This last statistic (88 for 3) comes from statistician Mario Cortina Borja in an article he wrote for the latest issue of Significance detailing “The strong birthday problem,” that is, not just one person but everybody in a group sharing a birthday with at least one other.  By assuming that the birthdays follow a uniform distribution,* Borja worked out this complex problem.  His results are somewhat counter-intuitive in the way probabilities decrease from 2 to 365 and rise thereafter—quickly gaining at 2000 and beyond.  (Of course if only “me, myself and I” are gathered, that is, one person, the probability is technically 100 percent of a birthday match.)  The answer to this strong birthday problem is 3064.  At 4800 people there’s a 99% chance that everyone will share a birthday with another.

Borja suggests that it might be fun for a large celebration to award a prize to anyone with a lone birthday.  If one won such a contest, it would really be a lonely experience.

*P.S. Borja provides the math for birthdays being distributed non-uniformly, but leaves it at that because the computational cost of solving it is “fiendish.”  That’s OK because other statisticians who studied this problem found that the results change very little with deviations from the uniform distribution.

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85 people have as much money as 3.5 billion

The 3.5 billion poorest people who account for half the world’s population can barely scrape up enough money to match the 85 wealthiest, according to the international relief organization Oxfam.  I await verification on this statistic but, if true, it really boggles my mind.

Oxfam teed this attention-getting shot up in prep for the annual World Economic Forum in Davos, Switzerland this week.  Let’s hope this convocation brings out the gnomes from Zurich who manage the gold from the hive of the weighty eighty-five.  Perhaps a few coins might trickle out from the greedy to the needy.

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Another round of three deaths now underway—triggered by the Professor

My favorite character in Gilligan’s Island–the Professor (aka Dr. Roy Hinkley)—passed away recently. 🙁 Who else will die, I wonder, because these always come in threes, or so it seems.

According to this newly-published study explaining “When Three Charms…, people gravitate to number 3.  Being business school profs (Suzanne B. Shu of UCLA and Kurt A. Carlson  of Georgetown U.), the authors focused on how to exploit this phenomenon for marketing purposes—their experiments pointing to the power of persuasion being optimized at three claims and no more—the fourth one pushes consumers over to being over-sold.

So be on guard from now on whenever someone tries to sell you on something by touting three reasons. 😉

Getting back to the morbid fascination with celebrity deaths, it may just be that this occurs from the natural tendency to conclude that three events in a row cannot happen just due to chance.

“You reach maximum streakiness at three events.”

–          Kurt Carlson quoted by New York Times in 1/3/14 article about The Power of Three

Being somewhat savvy on statistics and generally a rational thinker, I know this is immensely overblown, but I cannot help but succumb to it, in particular when bad things come in bunches.  My trick to put a halt to being unlucky is to resolve that whenever I’m hit by three unpleasant events then I watch for three good things to come.  I suppose this is just the power of positive thinking overcoming the depressive impact of cursed karma, but this works for me—I encourage you to give it a try.

When the bunch of bad reaches three, that’s it for me–make that your mantra.    🙂

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