Estimate a Population Total From a Sample

Estimating a Population Total

When you know information from a sample and want the total for the whole population, use the sample to estimate a larger whole. The key idea is to first find what one unit represents, then scale up to all units.

1) Identify the sample information

Look for:

• the number of items in the sample
• the value, count, or amount found in that sample
• the total population size

Make sure you are using matching units and the correct population count.

2) Find the sample proportion or average, if needed

If the problem gives a count in the sample, turn it into a rate or proportion by dividing by the sample size. If it gives an average amount per item, use that average directly.

3) Scale to the whole population

Multiply the sample rate or average by the population size.

• For a proportion: estimated total = population size × sample proportion
• For an average amount: estimated total = population size × sample average

4) Simplify the result

Carry out the arithmetic carefully and simplify the final number as requested.

5) Check your answer

Ask whether the estimate is reasonable:

• Does it stay in the right size range?
• If the sample rate was small, is the total still smaller than the population size when appropriate?
• Are you estimating a count, not a percentage?

A good estimate should match the pattern in the sample and use the whole population size correctly.