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.
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.
Subtract the lowest score in the set from the highest score in the set. That is,
$\text{Range }=\text{Highest Score}-\text{Lowest Score}$Range =Highest Score−Lowest Score
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.
Practice questions
Question 1
Find the range of the following set of scores:
$10,19,19,7,20,14,2,11$10,19,19,7,20,14,2,11
Question 2
The range of a set of scores is $8$8, and the highest score is $19$19.
What is the lowest score in the set?
Question 3
In a study, a group of people were shown $30$30 names, and after $1$1 minute they were asked to recite as many names by memory as possible. The results are presented in the dot plot.
Each dot represents:
One person in the group
AOne name remembered
BHow many people took part in the study?
What is the largest number of names someone remembered?
What was the smallest number of names someone remembered?
What is the range?