Question

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

Explanation:

Step1: Arrange data in order

The data set 1, 1, 1, 1, 3, 3, 5, 6 is already in ascending - order.

Step2: Find the median (Q2)

There are \(n = 8\) data points. The median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=4\) and \(\frac{n}{2}+1 = 5\). So, \(Q2=\frac{1 + 3}{2}=2\).

Step3: Find Q1

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

Step5: Calculate the inter - quartile range (IQR)

\(IQR = Q3 - Q1\). Substitute \(Q1 = 1\) and \(Q3 = 4\) into the formula. \(IQR=4 - 1=3\).

Answer:

3