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

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]