
Title:
Get to Know the PDF  Intro to Descriptive Statistics

Description:

We can do the same with normal distributions, which are modeled by a special

probability density function. We're not going to go over the equation for this

probability density function in this course. But if you want, you can easily

look it up and see what it is. And that might be pretty cool for some of you

who want a little more information. But basically, since we have this

theoretical curve, we can model it with an equation. And using this equation,

we can use Calculus with a curve. But, we don't need to use Calculus, because

someone else already did. And then, they created a special table, so we can

always figure out the area under the curve between any two value. We're going

to use this table later. First, let's make sure we're all up to speed on the

normal probability density function and the area underneath. First, the tails

never actually touch the xaxis, they get closer and closer to the xaxis. So,

the xaxis is a horizontal asymptote. The reason the tails of this thoretical

model don't touch the xaxis is basically because we can never be 100% sure of

anything. In other words, we could have a value way out here, really far from

the mean, like five standard deviations away. But the probability of getting

this value or lower is very small. And it's equal to the area under the curve.

So, if we could zoom in, we would see this tail get closer and closer to the

xaxis but never touching. And then, the area in between the tail and the

xaxis, all the way to negative infinity is the probability of getting this

value or lower. We'll go more into depth in that in a second. And similarly, we

could get a value way out here. But the probability is very small. So

basically, what you have to remember is that if we have a certain value, let's

just call it x for now. That the area under the curve from negative infinity to

x is equal to the probability of randomly selecting a subject in our sample

less than x. And this is equal to the proportion in the sample or population

with scores less than x. If this probability is 80%, then we say x is the 80th

percentile. If this probability is 90%, we say x is the 90th percentile, etc.

If this is a little confusing, don't worry. That's the whole point of this

lesson. You're going to get really comfortable with using the probability

density functions and analyzing this area, and finding this area.