Question

in the data set below, what is the interquartile range? 1 3 9 3 4 9 9

Explanation:

Step1: Sort the data

Sort the data set \(1,3,9,3,4,9,9\) in ascending order: \(1,3,3,4,9,9,9\).

Step2: Find the median (Q2)

Since there are \(n = 7\) data points, the median (the \(4^{th}\) value) is \(Q2=4\).

Step3: Find Q1

The lower - half of the data is \(1,3,3\). The median of the lower - half (for \(n = 3\), the \(2^{nd}\) value) is \(Q1 = 3\).

Step4: Find Q3

The upper - half of the data is \(9,9,9\). The median of the upper - half (for \(n = 3\), the \(2^{nd}\) value) is \(Q3=9\).

Step5: Calculate the inter - quartile range (IQR)

The formula for the inter - quartile range is \(IQR=Q3 - Q1\). Substitute \(Q1 = 3\) and \(Q3 = 9\) into the formula: \(IQR=9 - 3\).

Answer:

\(6\)