Question

in the data set below, what is the interquartile range? 63 76 69 59 21 96 24 88 28 43 10

Explanation:

Step1: Sort the data set

$10, 21, 24, 28, 43, 59, 63, 69, 76, 88, 96$

Step2: Find the median (Q2)

Since there are 11 data - points, the median is the 6th value. So, $Q2 = 59$.

Step3: Find the lower half and Q1

The lower half is $10, 21, 24, 28, 43$. The median of the lower half (Q1) is the 3rd value, so $Q1 = 24$.

Step4: Find the upper half and Q3

The upper half is $63, 69, 76, 88, 96$. The median of the upper half (Q3) is the 3rd value of this half, so $Q3 = 76$.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q3 - Q1=76 - 24 = 52$

Answer:

$52$