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 manager takes down information about the number of patients who missed appointments at one GP practice.
In order to find the range of this data, you simply find the biggest value (12 ) and the smallest value (2) and find the difference:
12 – 2 = 10
The range is therefore 10.
Now let’s compare this GP practice to a different practice shown below.
This practice has a highest value of 7 and a lowest value of 3. The range for this practice is therefore 7 – 3 = 4. The patients at the second practice are therefore more consistent as turning up for their appointments.
Now try one for yourself.
Activity 9: Finding the range
The day care centre you work at has a café for clients and their relatives. The table below shows the sales made by the café on each day of the week:
What is the range of sales for the café over the week?
The class teacher has asked you to look at the range of children’s’ scaled SATs scores in order to work out who is at most need of intervention sessions. The table below shows the scores for some children.
Which player is the most consistent? Give a reason for your 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 child:
Sam: 115 − 102 = 13
Amina: 100 − 84 = 16
Freddie: 116 − 1142 = 4
Amy: 92 − 87 = 5
Samir: 107 − 99 = 6
The child with the highest range is Amina and therefore she is the least consistent. She is therefore at most need of intervention sessions.
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.