Normal Distribution

Some people call it The Bell Curve. Others call it the Normal curve. Some people even call it Steve. That last group is a bunch of idiots, as the Normal distribution only goes by Stephen. Duh.

The normal distribution is a continuous probability distribution, where the event with the highest probability is located at the mean, and events of lesser probability are located away from the mean.

Okay, so…how far someone can kick a football is, approximately, a Normal distribution. We've got a bunch of average joes who can kick a football a certain distance. Maybe 20 to 40 yards. A bunch of people can do this…like, zillions probably. Ish. Then we have old, Legless Joe. He can kick the ball…maybe a yard? If he gets lucky and manages to flail and hit it as he's falling? Of course, on the other end, there's also Kicky, the Cyborg sent from the future to kick footballs and chew bubblegum. And yeah, he's all out of bubblegum. He can kick the ball 90 yards.

The point is that we have a bunch of stuff in the middle, and very little stuff way out on either end. There there's stuff that's not Normal...like rolling a six-sided die a bunch of times. We're not gonna get a crapload of 3s and 4s, and very few 1s and 6s. We're gonna get roughly equal amounts of each.

Stuff that's also approximately Normal? The number of Skittles in the standard-sized bag. Most bags have around maybe 90 Skittles. But some bags have like 95, or even 100. Bonus Skittles! Other bags only have 80…or 70. But most of the bags will have around 90, while bags that have values greater than or less than 90 are less and less common the farther we get from the mean.

Stuff that's also not Normally-distributed? How much money people spend at Mickey D's at lunch. We'll have a bunch of people buying a combo meal, so around 6 bucks. Very few will spend less. But then we'll have the guy ordering for his office, who racks up like a 40-dollar total. Or maybe 70 dollars or more. We end up with a huge bulge around the single combo meal price, with all these weird, higher-dollar values that sit far away from the group. They're not balanced out by small values on the other side of the bulge.

There's a good chance we have a Normal distribution, or at least something very close to it, when we meet two conditions. First, we must have one particular measurement or result that shows up more of than any other. The most common blobfish length might be 10 inches. We should get more 10-inch blobfish than any other height.

Second, as we get measurements both larger and smaller than that most common value, we see fewer and fewer of those larger and smaller results, i.e., as we get blobfish farther and farther from 10 inches in length, either smaller or larger, we'll see fewer and fewer of those on the hook. Specifically, to match the Normal distribution, we need to see the number of different-sized blobfish broken down this way:

65% of the blobfish must fall between negative one and positive one standard deviations on either side of the mean.

95% of the blobfish must fall between negative two and positive two standard deviations on either side of the mean.

99.7% of the blobfish must fall between negative three and positive three standard deviations on either side of the mean. This is called the Empirical Rule. It's, um...also not called Steve.

Take the dough used at Subway to make their subs. You'll realize that, even though the dough balls are all supposed to be the same size, they're not. The doughballs are supposed to weigh exactly 10 ounces. In reality, they come both larger and smaller, with 10 ounces being the most common weight that shows up. Weights significantly far away from 10 ounces, like 9.5 ounces, for example, are uncommon.

Still, they do show up at that size. In fact, the doughball weights are Normally distributed with a mean of 10 ounces and a standard deviation of 0.28 ounces. Let's pretend Subway instituted some quality control beyond just measuring their footlongs to ensure they're actually a foot long. Right, we know that’s a pipedream, too. But…maybe they decide that any doughball under 9.5 ounces is too small to make a decent loaf. Those wee doughballs need to be tossed back to be...re-doughed.

And then...enter a lot of math. Which...we're not going to get into here. Take a statistics class (or watch our video) if you want to get your fill.