# Poopy Statistics

Most who read this blog know me as an English teacher. However, what some may not know is that I have taught at least one math course for all 9 years of my teaching career, including next year. In fact, I have taught every math course I am certified to teach: 6th, 7th, and 8th grade math, Pre-Algebra, Algebra I, Geometry, Algebra II, Trigonometry / Pre-Calculus, Calculus, and Statistics. I am even helping out with our AP Physics class next year, as it is a math-heavy course. I love math.

So math is where my mind was at when I came across this joke the other day (paraphrased):
“It’s skewed a bit by my first couple years, but I still poop my pants 22 times a year on average.”

I love this joke. I’m going to be 31 years old next month, and I probably poop my pants, on average, over 32 times a year.

The key, of course, is in the words “on average.” I’m definitely going to have my students calculate this for themselves next year in my stats course. Here’s what I did:

First, I needed an estimate of how many times I pooped my pants/diaper as an infant. Having a newborn of my own, I have a pretty good idea that this is way more than I thought humanly possible. A number my wife and I are often told is healthy is three times a day, at least for the first three months or so, when it begins to lessen. So for the first three months of my life, I probably pooped my pants about 90 times.

Fun fact: as I was typing that last sentence, my son pooped his pants.

Let’s be conservative with the rest of the poops. Maybe I pooped about once a day until I was 2, and then, like magic, I was potty-trained (crossing my fingers that this happens with my own son!). This gives us 730 pooped pants.

But let’s be honest. That number isn’t right. It’s probably actually over 1000 (I’m pretty sure my son is over 1000 already, and he’s not even 4 weeks old). So let’s just go ahead and settle on 1000 poops. It’s a nice number, easy to remember.

So I have pooped my pants 1000 times. Over 31 years of my life, that is — on average — over 32 times a year.

The reason I love this joke is because I can use it to help my students think about the measures of center, and which ones really make sense to use. Yes, I can say I still poop my pants, on average, 32 times a year, but that’s certainly not the case (I max out at like 25 or so, I swear). So which measure of center makes sense to use here? The mean (often called “the average”)? The median? The mode?

The default example for this seems to be income levels, with one worker making over a million dollars and everyone else making around \$30,000. Trust me: that has no basis to our students. But tell them they poop their pants over 50 times a year, and I promise you you’ll have their attention.

And there’s even a bonus linear modelingÂ question! If someone poops their pants an average of 22 times a year, and we assume they pooped 1000 times as an infant, how old are they likely to be? I’ll leave that one for you to work out on your own.