Levels of measurement - what you can and can't do arithmetically

# 6. Activity - exploring permissable operations

Here’s a spreadsheet listing a number of people. Females are assigned 1 and males 2. Their heights, temperatures and shoe sizes are also recorded. The shoe sizes are converted to mm using a look up table.

Click on the total boxes for each column to see what’s permitted.

Name | Sex | Height (m) | Temp °C | Shoe Size | Shoe Size (mm) |
---|---|---|---|---|---|

Anne | 1 | 1.46 | 36.86 | 4 | 245 |

Tim | 2 | 1.87 | 37.02 | 10 | 298 |

Mathew | 1 | 1.76 | 37.07 | 8 | 278 |

Sheila | 1 | 1.34 | 36.78 | 5 | 252 |

Soraya | 1 | 1.70 | 36.64 | 6 | 260 |

Ben | 2 | 1.77 | 36.97 | 9 | 286 |

Bob | 2 | 1.89 | 37.01 | 11 | 305 |

Sue | 1 | 1.82 | 36.83 | 8 | 278 |

Total? | Yes No No | Yes No 13.61 | Yes No 295.18 | Yes No No | Yes No 2202 |

Mean? | Yes No No | Yes No 1.70 | Yes No 36.898 | Yes No No | Yes No 275.3 |

Median? | Yes No No | Yes No 1.77 | Yes No 36.915 | Yes No 8 | Yes No 278 |

### Shoe Size

Shoe size is tradionally an ordinal measurement but can be converted to a ratio measurement using a look up table.

Shoe Size | Euro | mm |
---|---|---|

4 | 37 | 245 |

5 | 38 | 252 |

6 | 39 | 260 |

7 | 41 | 270 |

8 | 42 | 278 |

9 | 43 | 286 |

10 | 45 | 298 |

11 | 46 | 305 |