Answer:
[tex] IQR =Q_3 -Q_1[/tex]
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:
[tex] Q_1 = \frac{38+45}{2}= 41.5[/tex]
And for the Q3 we can select the last 4 values 57, 63, 72, 91 and for Q3 we got:
[tex] Q_3= \frac{63+72}{2}= 67.5[/tex]
And then the interquartile range would be:
[tex] IQR =Q_3 -Q_1 = 67.5-41.5 = 26[/tex]
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:
[tex] IQR =Q_3 -Q_1[/tex]
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:
[tex] Q_1 = \frac{38+45}{2}= 41.5[/tex]
And for the Q3 we can select the last 4 values 57, 63, 72, 91 and for Q3 we got:
[tex] Q_3= \frac{63+72}{2}= 67.5[/tex]
And then the interquartile range would be:
[tex] IQR =Q_3 -Q_1 = 67.5-41.5 = 26[/tex]
