Question

in the data set below, what is the interquartile range? 5 4 5 7 9 6 4 6 1 1 2

Explanation:

Step1: Sort the data

Sort the data set \(1,1,2,4,4,5,6,6,7,9\).

Step2: Find the median

The median (\(Q_2\)) of the sorted data (with \(n = 11\) values) is the \(\frac{n + 1}{2}=6^{th}\) value. So \(Q_2=5\).

Step3: Find \(Q_1\)

The lower half of the data is \(1,1,2,4,4\). The median (\(Q_1\)) of the lower half (with \(n = 5\) values) is the \(\frac{n+1}{2}=3^{rd}\) value. So \(Q_1 = 2\).

Step4: Find \(Q_3\)

The upper half of the data is \(6,6,7,9\). The median (\(Q_3\)) of the upper half (with \(n = 4\) values) is the average of the \(2^{nd}\) and \(3^{rd}\) values. \(Q_3=\frac{6 + 7}{2}=6.5\).

Step5: Calculate the inter - quartile range

The inter - quartile range \(IQR=Q_3-Q_1\). So \(IQR = 6.5-2=4.5\).

Answer:

\(4.5\)