Question

in the data set below, what is the interquartile range? 1 4 6 9 8 4

Explanation:

Step1: Sort the data

Sort the data set \(1,4,6,9,8,4\) in ascending order: \(1,4,4,6,8,9\)

Step2: Find the median

Since there are \(n = 6\) data points, the median is the average of the \(3^{rd}\) and \(4^{th}\) values. The lower half is \(1,4,4\) and the upper half is \(6,8,9\)

Step3: Calculate \(Q_1\) and \(Q_3\)

For the lower half \(1,4,4\), \(Q_1=4\). For the upper half \(6,8,9\), \(Q_3 = 8\)

Step4: Compute the inter - quartile range

The inter - quartile range \(IQR=Q_3 - Q_1\). Substitute \(Q_1 = 4\) and \(Q_3=8\) into the formula: \(IQR=8 - 4\)

Answer:

\(4\)