Question

in the data set below, what is the interquartile range? 13 15 22 29 57

Explanation:

Step1: Find the median

The data set is \(13,15,22,29,57\). The median is the middle value. Since there are \(n = 5\) values, the median \(Q_{2}=22\).

Step2: Find \(Q_{1}\)

The lower - half of the data is \(13,15\). The median of the lower - half (\(n = 2\)) is \(Q_{1}=\frac{13 + 15}{2}=14\).

Step3: Find \(Q_{3}\)

The upper - half of the data is \(29,57\). The median of the upper - half (\(n = 2\)) is \(Q_{3}=\frac{29+57}{2}=43\).

Step4: Calculate the inter - quartile range (IQR)

The formula for the inter - quartile range is \(IQR=Q_{3}-Q_{1}\). Substitute \(Q_{1}=14\) and \(Q_{3}=43\) into the formula: \(IQR = 43-14\).

Answer:

\(29\)