Hello everyone and welcome back.

Now that we've talked about some characteristics of continuous data

and how to summarize it in the last lecture section,

and we also talked about various distributional shapes we might

encounter including roughly symmetric and bell-shaped,

left skewed and right skewed for example,

we're going to talk now about a very specific theoretical distribution that

many of you have probably heard of but we're going to

look at some characteristics of it in detail.

And that the distribution I'm talking about is called

the normal distribution or sometimes the Gaussian distribution.

So, we're first going to define

this theoretical distribution and look at some properties of it, specifically,

with regards to how far we need to go from the mean of the distribution

in either direction to capture

certain percentage of the data that follow that distribution.

So, for example, we'll see that on normal distributions,

if we start at the center and which is the mean and

we go plus or minus two standard deviations in either direction,

that interval will contain roughly 95 percent of

the observations described by that distribution.

Once we've established these properties,

we'll look at applying these ideas to situations where we have

a data set that's well approximated by a normal distribution.

We'll talk about why no real life data can perfectly follow

a normal distribution but there are situations

where the data like we saw with the blood pressures for example,

they're roughly symmetric and bell-shaped around

their center and we can use characteristics of the normal distribution,

the theoretical normal distribution to estimate characteristics

of the sample distribution using only the mean and standard deviation.

And then finally, we'll say this is all

good but it only again works when we have data that are

approximately normal and will show that if we miss

apply some of these properties of the data that are not normal for

example are heavily skewed and try and make statements about data

ranges in our sample using

just the mean and standard deviation and invoking the properties of the normal curve,

we'll get nonsensical ridiculous results.

And so, it'll just serve as a warning to not to blindly use the relationship

between the mean and standard deviation for

normal curves and apply it to non-normal data.

The reason we're talking about this now is both

that fits into the context of continuous data measures that we're working on

but we're going to see later in the course that there are

some theoretical distributions that we can't observe directly but we'll know are

normal in shape and we can estimate their mean and standard deviation and we can

put those three ideas together and make statements

about this distribution we won't be able to directly observe.

So, hopefully that what your appetite for learning more about this famous some

might say infamous distribution and onward and upward with the normal curve.