Normal Distribution Curve

People often tell us that we're more than three deviations away from normal. According to the curve, that means we're cooler than 98% of the population! Nerds do come out on top.

LanguageEnglish Language
StatisticsEvaluating Data

Transcript

00:22

…but we’re more interested in Normal in the mathematical sense.

00:27

The normal curve looks like this. It’s the bell shaped graph that results when statisticians

00:32

plot data with a… normal distribution. Basically, the total area under the curve

00:40

equals… one.

00:43

This area is divided up into standard deviations… the areas to the left and right of the middle

00:52

of the curve…

00:53

…and it also happens to be the average of the data.

00:57

Take male height for example.

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The average height of an adult male is seventy inches, or five feet ten inches, with a standard

01:03

deviation of four inches.

01:05

That means that sixty-eight point two percent of all males are within four inches of five

01:12

foot ten. These guys are considered “normal.”

01:18

Unfortunately for Gene, at six foot five, he falls two deviations away from the average.

01:25

The second deviation from either side of the midpoint makes up twenty seven point three

01:30

percent of the area under the curve.

01:32

In Gene’s case, he falls into the twenty seven point three percent of the population

01:36

who is either shorter than five six or taller than six two.

01:40

So he has to shop at one of these. At least Gene still falls into the ninety

01:45

five point five percent of the population within two standard deviations of the average.

01:52

But what about that other four point five percent? Who are those guys?

01:56

Anyone shorter than five two or taller than six six will land three standard deviations

02:02

from the average.

02:03

These guys make up four point two percent of the population.

02:07

That means that ninety-nine point eight percent of men stand within three standard deviations

02:13

of five feet ten inches tall. So Gene may not fall within one deviation

02:18

for height… but what about his other features?

02:21

Maybe nose length? Whoa, nope.

02:25

How about hair color? Sorry, don’t think Gene will be with the majority on that one

02:28

either.

02:29

Hey, wait a minute. With that big head of his he’s got to have a decent IQ, right?

02:34

Let’s see where the Green Bean falls.

02:37

The average IQ score is one hundred.

02:39

The standard deviation is fifteen points, so does Gene fall within one standard deviation?

02:45

Sweet! Gene, with his barely above average IQ…

02:49

…can join sixty eight point two percent of the population within one standard deviation

02:54

of the average.

02:54

Congratulations, average pants!