1.12 Looking ahead

So far we have treated the sample as though it were the population. The average age, average income or average height was simply computed from the data in front of us.

In practice the sample is only one of many that might have been drawn.

Suppose you collect a random sample of fifty households and find an average monthly income of ₹24,000.

Should ₹24,000 be your estimate of the population average? Why not ₹23,800, or ₹24,500? What makes one estimate better than another?

You might think the answer is obvious: use the sample mean.

But why the sample mean? Why not the median? Why not the largest observation, or some weighted average of the fifty?

Before we can measure uncertainty, we need to understand why the sample mean deserves to be called an estimate at all. That is the subject of the next unit.