Wednesday, October 17th, 2012...11:00 am

Getting Mean about Bill Gates

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Suppose you are at a Major League Baseball game and your friend is looking through binoculars for celebrities. Suddenly, your friend turns and comments, “Did you know that the average person at this game is a millionaire?” How would you respond? Who did your friend see in the stands?

Turns out if Bill Gates, as seen to the left from his Twitter picture, attended a baseball game, regardless of the stadium, then the average net worth for someone at the game would be over a million dollars.

According to Wikipedia, Bill Gates’ net worth in 2012 is 66 billion. Also according to Wikipedia, the largest baseball stadium is Dodger Stadium holding 56,000. So, a fan at Dodger Stadium, if Bill Gates attended the same game, would have an average net worth of 61,000,000,000/56,000 > 1,000,000.

Now, suppose Bill Gates made his way into Michigan Stadium which holds 107,501. In this case, fans have an average net worth of 61,000,000,000/107,501, which is about 613,947. This is an impressive amount of money but a bit disappointing if one had attended the MLB game! But, this assumes that everyone other than Bill Gates has a net worth of 0. What would it take to raise the average to a million?

Take a moment and reflect on this question. It’s admittedly a bit mean! The average now plays the same role as before. To get to the million, the average must increase by 386,053. So, we need to find x such that (61,000,000,000 + 107,500x)/107,501. This implies that the average net worth of everyone else in the stadium must be 432,567, which is a pretty healthy sum of its own.

Now, what if Bill Gates walks in a bar?

This blog entry was inspired by @MathPlus’s tweet, “‘If Bill Gates walks into a bar, everyone [in the bar] is on average a millionaire.’ Roberton Williams #statistics #joke #Microsoft #fb” Thanks also to the Charlotte Teachers Institute fellows in my Entertaining Math seminar for encouraging me to write this entry.

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