# 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. It shows how spread out a set of data is and 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 – meaning their scoring is **variable**) 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 apple farm.

## Table 12

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.

## Table 13

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 has a lower range than the first worker and is therefore a more consistent apple picker than the first worker, who is a more variable picker.

Now try one for yourself.

## Activity 11: Finding the range

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

### Table 14

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?

### Answer

Simply find the highest value: £254.70, and lowest value: £156.72, then find the difference:

- £254.70 − £156.72 = £97.98

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

### Table 15

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

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.

Outside temperatures at a garden centre were taken daily over four weeks in January and displayed in the following table.

### Table 16 Temperatures for January in ˚C

Mon | Tue | Wed | Thu | Fri | Sat | Sun | |
---|---|---|---|---|---|---|---|

Week 1 | 2 | 4 | 5 | 5 | 1 | −1 | −3 |

Week 2 | −4 | 0 | 0 | 3 | 6 | 5 | 6 |

Week 3 | 3 | 2 | −1 | 0 | 3 | 2 | 0 |

Week 4 | 0 | 4 | 7 | 8 | 3 | −1 | −2 |

a.Which day of the week showed the most variable temperature range?

b.Which day of the week showed the most consistent temperature range?

c.Which days had the same range?

### Answer

a.Sundays had a lowest temperature of −3˚C and a highest temperature of 6˚C so the difference was 9˚C, giving Sundays the highest range and making temperatures more variable.

b.Tuesdays had a lowest temperature of 0˚C and a highest temperature of 4˚C so the difference was 4˚C, giving Tuesdays the lowest range and making temperatures more consistent.

c.Wednesdays and Thursdays had the same range.

Wednesdays had a lowest temperature of −1˚C and a highest temperature of 7˚C so the difference was 8˚C.

Thursdays had a lowest temperature of 0˚C and a highest temperature of 8˚C so the difference was 8˚C.

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.