Weekly turnover in a city with...

• 50 grocery stores from large chains
• 50 smaller independent grocery stores


Use this diagram to show how stratified sampling reduces variability in the sample mean (and hence improves accuracy) when the strata have different means.

Click Take sample. This takes both a simple random sample (left) and a stratified random sample (right).

Take several more samples and observe that the mean from the stratified sample is less variable (more accurate). Click on the largest and smallest of the sample means from the simple random samples to see the stores that were samples. Observe that they occur when a disproportionate number of large or small stores are sampled (by chance).

The diagram also shows the theoretical distributions of the means (or at least normal approximations to them).

The same improvement occurs when estimating the total grocery turnover in the city — 100 times the mean.


The data are not real and the differences between the two types of store are greater than would be seen in practice.

However the data do illustrate the advantages of stratified sampling well.