4.04 Range

Measures of spread in a numerical data set seek to describe whether the scores in a data set are very similar and clustered together, or whether there is a lot of variation in the scores and they are very spread out.

There are several methods to describe the spread of data, which vary in complexity. We can simply look at the numerical range of the entire data set–the difference between the largest and smallest value, or we can break the data into chunks (such as quartiles, deciles, or percentiles) to examine the range of smaller sections within the data. We can also compare the spread of data to the mean.

In this section, we will look at the range as measure of spread. 

Range

The range is the simplest measure of spread in a numerical data set. It is the difference between the maximum and minimum scores in a data set.

Exploration

For example, at one school the ages of students in Year $7$7 vary between $11$11 and $14$14. So the range for this set is $14-11=3$14−11=3 years.

As a different example, if we looked at the ages of people waiting at a bus stop, the youngest person might be a $7$7 year old and the oldest person might be a $90$90 year old. The range of this set of data is $90-7=83$90−7=83 years, which is a much larger range of ages.

How do scores affect range?

Remember, the range only changes if the highest or lowest score in a data set is changed. Otherwise it will remain the same. This will mean it will be significantly affected by an outlier being present in the data. Including an outlier will increase the range.

Practice questions

Question 1

Question 2

Question 3