Usually, an estimated total has got this form right here.

We sum up the units in the sample, we take the weight that we assign them,

times their data value.

And assuming again that these weights are scaled to estimate population

totals then we'll get a legitimate estimate of the finite population total.

We can estimate other things.

Means are interesting quantities.

We might want to estimate the average income,

the average number of years of schooling per person,

students' average test score on some standardized test.

The standard way of doing that is to take an estimate of the total.

That's this first piece, the sum over the sample of the weights times the data.

And then divided by the sum of the weights.

So you can see that these scales thing is it about the right way.

But one thing to note here,

the weights are normally calculated, the sum of the weights

is going to be an estimate of the number of units in a population.

Sometimes it's exactly equal to the number of units in the population,

it depends on how we calculate the weights and what type of samples is drawn.