Question

in the data set below, what is the interquartile range? 85 84 74 93 74

Explanation:

Step1: Sort the data

Sort the data set \(74,74,84,85,93\).

Step2: Find the median

The median \(Q_2\) is the middle value. Here, the median is \(84\).

Step3: Find \(Q_1\)

The lower half of the data is \(74,74\). The median of the lower half \(Q_1 = 74\).

Step4: Find \(Q_3\)

The upper half of the data is \(85,93\). The median of the upper half \(Q_3=\frac{85 + 93}{2}=89\).

Step5: Calculate the inter - quartile range (IQR)

The formula for \(IQR\) is \(IQR=Q_3 - Q_1\). Substitute \(Q_1 = 74\) and \(Q_3 = 89\) into the formula: \(IQR=89-74 = 15\).

Answer:

\(15\)