Now, that was all looking at sample data sets and

working with some sample statistics related to them.

We then sort of revisited part of our week 2 material, whereby we introduced

a further theoretical probability distribution, ie the normal distribution.

And said how useful it is for modeling many real-world phenomena.

And going forward in your statistical studies,

you'll see the normal distribution making frequent appearances

as distributional assumptions in a wide variety of models.

And to come later on in this course,

using something called the essential limit theorem, so more on that next week.

But we introduced the normal distribution as a two-parameter family, requiring or

distinguishing the different members of the normal family by the mean, mu,

and the variance, sigma squared, of these normal distributions.

We then went back slightly theoretically and

continued some of our week 2 material about how we could work out the variance,

based on a theoretical population distribution.

So this extended our definition of the sample variance,

which we viewed as an average of the square deviations about the sample mean.

And we saw the equivalent sort of expected value.

And we looked at the score of a fair die to work out the variance,

based on that simple probability distribution.

We then rounded off with a look at how we may

wish to benefit from standardizing our variables.

And noting that when we consider data on a standardized basis,

it's very easy to judge whether or not we have any extreme observations.

Remembering, on a z-score, values lying beyond plus or minus 2, or

indeed, beyond a plus or minus 3, we might look at defining as outliers, or

extreme outliers, respectively.

So looking ahead to week 4,

we are now in a position to start to conduct some formal statistical inference.

And that's going to occupy us for the next couple of weeks of the course.

We begin with issues of sampling from a population, and

how that could take place, as well as matters of point and interval estimation.

That will be week 4, and

then we're going to have a little look at hypothesis testing in week 5.

So bear in mind, there's a cumulative nature to probability and

statistics, and some of the themes we've seen already will be revisited and

seen again in our later work.

So join me for week 4, when we start our look at statistical inference.

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