Question

in the data set below, what is the interquartile range? 36 21 40 21 27

Explanation:

Step1: Sort the data

Sort the data set \(21,21,27,36,40\).

Step2: Find the median

The median \(Q_2\) is the middle value. Since there are \(n = 5\) values, the median is the third value. So \(Q_2=27\).

Step3: Find \(Q_1\)

The lower half of the data is \(21,21\). The median of the lower half (\(Q_1\)) is \(21\).

Step4: Find \(Q_3\)

The upper half of the data is \(36,40\). The median of the upper half (\(Q_3\)) is \(\frac{36 + 40}{2}=38\).

Step5: Calculate the inter - quartile range (IQR)

The formula for the inter - quartile range is \(IQR=Q_3 - Q_1\). Substitute \(Q_1 = 21\) and \(Q_3=38\) into the formula: \(IQR=38 - 21\).

Answer:

\(17\)