Question

what is the iqr of the following data set? 32, 38, 38, 40, 42, 44, 46, 48, 49, 60, 72 remember: the iqr is the difference between the upper and lower boundaries. a 6 b 11 c 5

Explanation:

Step1: Find the median

The data - set has 11 values. The median is the 6th value. So, the median $Q_2 = 44$.

Step2: Split the data - set

Split the data - set into two halves: the lower half $\{32,38,38,40,42\}$ and the upper half $\{46,48,49,60,72\}$.

Step3: Find $Q_1$ and $Q_3$

The median of the lower half is $Q_1$. Since there are 5 values in the lower half, the median (3rd value) is $Q_1 = 38$. The median of the upper half is $Q_3$. Since there are 5 values in the upper half, the median (3rd value) is $Q_3 = 49$.

Step4: Calculate the IQR

The inter - quartile range $IQR=Q_3 - Q_1$. So, $IQR = 49-38=11$.

Answer:

B. 11