Question

in the data set below, what is the interquartile range?
12 31 32 40 43 55 55 56 69 69 72

Explanation:

Step1: Confirm sorted data set

Data: $12, 31, 32, 40, 43, 55, 55, 56, 69, 69, 72$ (already sorted, $n=11$)

Step2: Find median (Q2)

Median is the 6th value: $Q2 = 55$

Step3: Calculate Q1 (lower median)

Lower half: $12, 31, 32, 40, 43$. Median is 3rd value: $Q1 = 32$

Step4: Calculate Q3 (upper median)

Upper half: $55, 56, 69, 69, 72$. Median is 3rd value: $Q3 = 69$

Step5: Compute interquartile range

$IQR = Q3 - Q1$
$IQR = 69 - 32$

Answer:

$37$