Question

in the data set below, what is the interquartile range? 10 13 24 36 37 71

Explanation:

Step1: Find the median

The data set is \(10, 13, 24, 36, 37, 71\). Since there are \(n = 6\) data points, the median is the average of the \(3^{rd}\) and \(4^{th}\) values. The lower half is \(10, 13, 24\) and the upper half is \(36, 37, 71\).

Step2: Calculate \(Q_1\) and \(Q_3\)

For the lower half (\(10, 13, 24\)), \(Q_1\) (the median of the lower half) is \(13\). For the upper half (\(36, 37, 71\)), \(Q_3\) (the median of the upper half) is \(37\).

Step3: Compute the inter - quartile range (IQR)

The formula for the inter - quartile range is \(IQR=Q_3 - Q_1\). Substitute \(Q_1 = 13\) and \(Q_3 = 37\) into the formula: \(IQR=37 - 13\).

Answer:

\(24\)