A stratified random sample is similar to a quota sample. The key difference is that the representatives from each category are chosen at random. In the previous section we looked at a quota sample that was made up of 4 boys and 6 girls.

In the *quota sample* the first 4 boys from the list were chosen and then the first 6 girls.

In a *stratified random sample* the 4 boys should be selected randomly from the 12 boys in the class. In the same way, the 6 girls should be selected randomly from the 18 girls in the class.

Take a stratified random sample of size 5 from the class considered in the earlier sections.

The class consists of 18 girls and 12 boys, 30 pupils altogether. We want a sample of size 5 so we need to include = of the girls, and of the boys. This means that we need to choose 3 girls and 2 boys.

We choose a random sample of 3 girls. The girls in the class are:

1 | Lucy | 7 | Hannah | 13 | Sophie |

2 | Jayne | 8 | Grace | 14 | Kathryn |

3 | Nadima | 9 | Lisa | 15 | Helen |

4 | Sushi | 10 | Sacha | 16 | Fatoumata |

5 | Rachel | 11 | Daniella | 17 | Annie |

6 | Emma | 12 | Anna | 18 | Karen |

Using random digits gives:

So the sample will contain:

3 | Nadima |

9 | Lisa |

15 | Helen |

The boys are:

1 | Alan | 5 | Mohammed | 9 | Joshua |

2 | Tom | 6 | Ben | 10 | Halim |

3 | Azar | 7 | Miles | 11 | Joseph |

4 | Matthew | 8 | James | 12 | Salif |

Using random digits gives:

Note that the second 7 is ignored.

So the sample will also contain:

7 | Miles |

2 | Tom |

The complete stratified random sample will therefore consist of

Nadima, Lisa, Helen, Miles and Tom.

A company has a total of 360 employees in four different categories:

Managers | 36 |

Drivers | 54 |

Administrative Staff | 90 |

Production Staff | 180 |

How many from each category should be included in a stratified random sample of size 20 ?

To create a sample of size 20 we need or of the workforce. So we take this fraction of the number of employees in each category.

Managers | × 36 | = | 2 |

Drivers | × 54 | = | 3 |

Administrative Staff | × 90 | = | 5 |

Production Staff | × 180 | = | 10 |

TOTAL | = | 20 |