# 6.1 Range

Much like this stunning mountain range is made up of a variety of different sized mountains, a set of numerical data will include a range of values from smallest to biggest. The range is simply the difference between the biggest value and the smallest value. The range can be useful to know because data sets with a big difference between the highest and lowest values can imply a certain amount of risk.

Let’s say there are two basketball players and you are trying to choose which player to put on for the last quarter. If one player has a large range of points scored per game (sometimes they score a lot of points but other times they score very few) and the other player has a smaller range (meaning they are more consistent with their point scoring) it might be safest to choose the more consistent player.

Take a look at the example below.

A farmer takes down information about the weight, in kg, of apples that one worker collected each day on his farm.

Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
---|---|---|---|---|---|---|

56 kg | 70 kg | 45 kg | 82 kg | 67 kg | 44 kg | 72 kg |

In order to find the range of this data, you simply find the biggest value (82 kg) and the smallest value (44 kg) and find the difference:

- 82 – 44 = 38 kg

The range is therefore 38 kg.

Now let’s compare this worker to another worker whose information is shown in the table below.

Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
---|---|---|---|---|---|---|

56 kg | 60 kg | 58 kg | 62 kg | 65 kg | 49 kg | 58 kg |

This worker has a highest value of 65 kg and a lowest value of 49 kg. The range for this worker is therefore 65 – 49 = 16 kg. The second worker is therefore a more consistent apple picker than the first worker.

Now try one for yourself.

## Activity 9: Finding the range

- The table below shows the sales made by a café on each day of the week:

Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
---|---|---|---|---|---|---|

£156.72 | £230.54 | £203.87 | £179.43 | £188.41 | £254.70 | £221.75 |

- What is the range of sales for the café over the week?

- A bowling team want to compare the scores for their players. The table below shows their results.

Name | Andy | Bilal | Caz | Dom | Ede |
---|---|---|---|---|---|

Highest score | 176 | 175 | 162 | 170 | 150 |

Lowest score | 148 | 145 | 142 | 165 | 116 |

- Which player is the most consistent? Give a reason for your answer.

### Answer

- Simply find the highest value: £254.70, and lowest value: £156.72, then find the difference:
- £254.70 − £156.72 = £97.98

- You need to look at the range for each player:
- Andy: 176 − 148 = 28
- Bilal: 175 − 145 = 30
- Caz: 162 − 142 = 20
- Dom: 170 − 165 = 5
- Ede: 150 − 116 = 34

- The player with the smallest range is Dom and so Dom is the most consistent player.

As you have seen, finding the range of a set of data is very simple but it can give some useful insights into the data. The most commonly used average is the ‘mean average’ (or sometimes just the mean) and you’ll look at this next.