6.3 H) Interquartile Range – Part 2
I asked 15 of my class members how long it took them to get to school in minutes. I obtained the following results:
What is the interquartile range for the data above?
We work out the interquartile range by taking the lower quartile from the upper quartile. Therefore, we need to work out what the lower and upper quartiles are. Before we do this, we should order the data from smallest to largest. This is shown below:
Now that we have the data ordered, we need to find which term in the ordered data is the lower and upper quartile. We find the lower and upper quartiles term by using the formulas that are at the top of this page. Both of the formulas contain the variable n, which is the number of values in the data set. There are 15 values, which means that we will be subbing in n as 15 into both of the formulas.
Let’s find which term is the lower quartile in the ordered data.
The lower quartile will be the 4th term in the ordered data.
The 4th term in the ordered data is 17. Therefore, the lower quartile is 17.
We now do the same for the upper quartile. We first need to find which term in the ordered data is the upper quartile. We are able to do this by subbing n as 15 into the formula below:
The upper quartile will be the 12th term in the ordered data.
The 12th term in the ordered data is 34. Therefore, the upper quartile is 34.
We now have both the lower (17) and upper quartile (34). This means that we are able to find the interquartile range by subbing these values into the formula below:
The interquartile range for the data is 17 minutes.