stratified sample

This is the name given to a sample which contains many ‘layers’ of a population.

For example, we can select samples from different age groups. The size of the sample is proportional to the size of the layer, as this equation shows:

    \text{Size of the sample for each layer} = \dfrac{\text{size of layer}}{\text{size of population}}\times \text{size of whole sample}

Here’s an example of a stratified sample.

There are 500 pupils in a school, and we need to ask 50 of them about their favourite food.

We must make sure that the survey is accurate, and therefore a range of pupils across the different school years is needed – these are the different ‘layers’.

The first table shows the number of pupils in each year.

Using the equation, we can calculate the size of the sample for each year.

    • There are 100 pupils in Year 7, therefore this is the size of the layer.

    • There are 500 pupils in the school, therefore this is the size of the population.

    • Answers are needed from 50 pupils, therefore this is the size of the whole sample.

Therefore, the number of pupils in the sample for Year 7 is 10, as \dfrac{100}{500} × 50 = 10.

We use this equation to calculate the size of the sample for Years 8–11.