Question

in the data set below, what is the interquartile range? 42 56 66 73 95

Explanation:

Step1: Find the median

The data set is \(42,56,66,73,95\). The median is the middle value. Here, the median \(Q_2 = 66\).

Step2: Find \(Q_1\)

The lower - half of the data (values less than \(66\)) is \(42,56\). The median of the lower - half is \(Q_1=\frac{42 + 56}{2}=\frac{98}{2}=49\).

Step3: Find \(Q_3\)

The upper - half of the data (values greater than \(66\)) is \(73,95\). The median of the upper - half is \(Q_3=\frac{73+95}{2}=\frac{168}{2} = 84\).

Step4: Calculate the inter - quartile range (IQR)

The formula for the inter - quartile range is \(IQR=Q_3 - Q_1\). Substitute \(Q_1 = 49\) and \(Q_3 = 84\) into the formula: \(IQR=84 - 49=35\).

Answer:

\(35\)