Question

in the data set below, what is the interquartile range? 7 2 2 4 7 6 4 2 5 1 3

Explanation:

Step1: Sort the data

Sort the data set \(1,2,2,2,3,4,4,5,6,7,7\).

Step2: Find the median

Since there are \(n = 11\) data points, the median (second - quartile \(Q_2\)) is the \(\frac{n + 1}{2}=6^{th}\) value. So \(Q_2=4\).

Step3: Find the lower half and \(Q_1\)

The lower half of the data is \(1,2,2,2,3\). The median of the lower half (first - quartile \(Q_1\)) is the \(3^{rd}\) value. So \(Q_1 = 2\).

Step4: Find the upper half and \(Q_3\)

The upper half of the data is \(5,6,7,7\). The median of the upper half (third - quartile \(Q_3\)) is the \(3^{rd}\) value of the upper half. So \(Q_3=7\).

Step5: Calculate the inter - quartile range (IQR)

The formula for the inter - quartile range is \(IQR=Q_3 - Q_1\). Substitute \(Q_1 = 2\) and \(Q_3=7\) into the formula: \(IQR=7 - 2\).

Answer:

\(5\)