## Stratified Sampling

Stratified sampling is a sampling method useful when the population to be sampled falls into distinct categories. It is desirable that the sample reflect the population,so that the proportion of each category in the sample reflects the proportion of that category in the population.

Suppose that school pupils are to be surveyed on their opinion of school dinners. The school has 1000pupils, and the sample size is to be 150. The pupils are categorised into sex and year groups as shown in the table below.

 Year Group Male Female 7 76 74 8 59 79 9 80 64 10 72 60 11 69 68 12 70 70 13 74 85

The formula for finding the number in each category to be sampled is

 Year Group Male Female 7 8 9 10 11 12 13

We must round the numbers in the table so that each is a whole number.

 Year Group Male Female 7 11 11 8 9 12 9 12 10 10 11 9 11 10 10 12 11 11 13 11 13

The numbers in the table add to 151 –1 more than the sample size of 150, but we have rounded both 10.5'sup. If we round one of them down, then the sample size is 150. The number in each category to be sampled is given in the table below.

 Year Group Male Female 7 11 11 8 9 12 9 12 10 10 11 9 11 10 10 12 11 11 13 11 13

Within each category, simple random sampling is used to select the pupils.