Tuesday, March 26, 2019

Statistics Isn't Useful

I'm teaching a statistics class this semester, so when I was watching basketball over the weekend with my son and saw a player from University of Central Florida named Tacko Fall, who is 7'6" tall, I wanted to know more. His Wikipedia page says he's "one of the tallest humans alive," but I wanted to know how many people are taller than he is. From assigning such problems to my students, I happened to know the average height of American males is 5'10" and the standard deviation is 2.9". Fall is 20 inches taller than the mean, which is 6.89 standard deviations above the mean.

Most Z-tables crap out at 3. I Googled "incredibly high Z scores" and all I found was stuff like, "If you end up with a really high Z score, the probability of something that extreme is zero." I Googled some more and found the equation that I would have to integrate from 0 to 6.89, and then subtract the answer from 0.5, but my integration days are past me and this equation had, like, an e to the power of negative something in an exponent. I Googled some more and found something that said, "If you have the statistical program R..." and I said excitedly, "I have R!" So I fired up R, entered the command, and hit "enter." And R said, "1." Meaning 100% of people are shorter than this. But Fall isn't the tallest person alive, so this isn't the answer I wanted.

Ultimately, I spent the entire first half of the game trying to answer this question, and I never figured it out.

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