Question

multiple choice
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 11
b 5
c 6

Explanation:

Step1: Find the median

The data - set has 11 values. The median is the 6th value when the data is in ascending order. So the median $Q_2 = 44$.

Step2: Find the lower half and its median ($Q_1$)

The lower half of the data set is $32,38,38,40,42$. The median of this lower - half ($Q_1$) is 38.

Step3: Find the upper half and its median ($Q_3$)

The upper half of the data set is $46,48,49,60,72$. The median of this upper - half ($Q_3$) is 49.

Step4: Calculate the IQR

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

Answer:

A. 11