Question

in the data set below, what is the interquartile range? 58 62 56 61 59 61

Explanation:

Step1: Sort the data

Sort the data set \(58,62,56,61,59,61\) in ascending order: \(56,58,59,61,61,62\).

Step2: Find the median

Since there are \(n = 6\) data points, the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. The median \(Q_2=\frac{59 + 61}{2}=60\).

Step3: Find \(Q_1\) and \(Q_3\)

The lower half of the data is \(56,58,59\), and the median of the lower half \(Q_1 = 58\). The upper half of the data is \(61,61,62\), and the median of the upper half \(Q_3=61\).

Step4: Calculate the inter - quartile range (IQR)

The formula for the inter - quartile range is \(IQR=Q_3 - Q_1\). Substitute \(Q_1 = 58\) and \(Q_3=61\) into the formula: \(IQR=61-58 = 3\).

Answer:

\(3\)