What is the interquartile range of the data set? {33, 38, 45, 56, 57, 63, 72, 91}

We have for this case n= 8 values. In order to find the Q1 we can select the first 4 values {33, 38, 45, 56 and the Q1 would be:

And for the Q3 we can select the last 4 values 57, 63, 72, 91 and for Q3 we got:

And then the interquartile range would be:

Step-by-step explanation:

For this problem we have the following dataset ordered:

{33, 38, 45, 56, 57, 63, 72, 91}

And we want to find the interquartile range defined as:

We have for this case n= 8 values. In order to find the Q1 we can select the first 4 values {33, 38, 45, 56 and the Q1 would be:

And for the Q3 we can select the last 4 values 57, 63, 72, 91 and for Q3 we got:

And then the interquartile range would be: