Question

in the data set below, what is the interquartile range? 1 1 1 1 1 1 3 3 3 5 5 6

Explanation:

Step1: Sort the data (already sorted)

1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 5, 6

Step2: Find the median (Q2)

There are 12 data - points. The median is the average of the 6th and 7th values. $\frac{1 + 3}{2}=2$.

Step3: Find Q1

The lower half of the data is 1, 1, 1, 1, 1, 1. The median of the lower half (Q1) is 1.

Step4: Find Q3

The upper half of the data is 3, 3, 3, 5, 5, 6. The median of the upper half (Q3) is $\frac{3+5}{2}=4$.

Step5: Calculate the inter - quartile range (IQR)

$IQR = Q3 - Q1=4 - 1 = 3$.

Answer:

3