Whereas the frame also contains some things that are not in the population,

that you can see the shadow there to the right and the bottom.

So, the frame is not a perfect representation, but

that's what we work with.

So, population to frame.

And then [COUGH] we have our list.

And from our list, this is a representation,

we've looked at this before, this is a more complete list of the faculty,

this is 150 of the 370 faculty from our example from the last lecture.

And in this particular case, that's the list that we're using.

And we don't know for sure whether we've missed some faculty who were newly

enrolled in the university, some others who have been removed from the list,

they've moved to other universities, they've passed on, whatever it might be.

There might be a mismatch between this list and

the actual set of faculty at the moment we're doing the sampling.

From that list, we draw a sample, that's the third step.

Okay, population, frame, sample.

That sample is a microcosm of the frame, and

we're going to do chance selections, right?

So, we're going to use something like a table of random numbers to draw that

sample from the frame.

And there's our random numbers, this is the full representation of a list that I

gave you just a little corner of when we were doing our example sample.

And it lead to a possible sample that had 20 cases and

there's the sequence numbers of those that were chosen that we did last time.

And I've added the incomes because now we've gone out and we've interviewed

these faculty and we've obtained their incomes and we've calculated the mean.

Way down at the bottom we can see the mean income.

Okay, that's the process we went through before.

Our process would involve population specification, a frame identification,

a random selection of a sample, and then computation of an estimate.

Those four steps.

And here we're on solid ground.

These are all things that we can physically represent.

But we also recognize that this sample [COUGH] and

the one mean that we've got probably isn't the true population value.

As a matter of fact, there's almost zero chance that that's the actual mean of

the population, because we got a sample of only 20 from 370.

There's some error,

there's some discrepancy between what we have in our sample and the population.

If we had done a census,

we'd done every one, then we would have the exact mean under this scheme.