## 2. Range

For a set of observations, the simplest measure of variability is the range - the difference between the smallest and largest values. Consider the datasets introduced earlier. For Set 1, the maximum value, x_{max} = 5.1, and the minimum value, x_{min} = 3.9. The range is given by:

range = x_{max} - x_{min} = 5.1 – 3.9 = 1.2

Note that the range is a quantity, a measure of variability, so does not have a sign – there is no such thing as 'negative' variability. The equation given here still applies to instances where one or both values are negative. For instance, if all of the values in Set 1 were negative, x_{max} = -3.9 and x_{min} = -5.1.

range = x_{max} - x_{min} = -3.9 – (-5.1) = -3.9 + 5.1 = 1.2

Looking at our three example datasets and some others:

x_{min} |
x_{max} |
Range | Median | Mean | |

Set 1 | 3.9 | 5.1 | 1.2 | 4.5 | 4.53 |

Set '1A' | -5.1 | -3.9 | 1.2 | -4.5 | -4.53 |

Set '4' | -5.1 | 3.9 | 9 | ||

Set 2 | 2.3 | 9.3 | 7 | 4.5 | 5.16 |

Set 3 | 2.3 | 9.3 | 7 | 6.9 | 6.3 |

The range is suitable as a measure of variability for scale (continuous as in the examples here, or discrete) or ordinal data.