Question

in the data set below, what is the interquartile range? 29 44 59 60 60 63 66

Explanation:

Step1: Find the median

The data set has 7 numbers. The median is the 4th number. So the median is 60.

Step2: Find \(Q_1\) (lower quartile)

The lower half of the data is \(29,44,59\). The median of this lower half (\(Q_1\)) is 44.

Step3: Find \(Q_3\) (upper quartile)

The upper half of the data is \(60,63,66\). The median of this upper half (\(Q_3\)) is 63.

Step4: Calculate the inter - quartile range (IQR)

The formula for IQR is \(IQR = Q_3-Q_1\). Substitute \(Q_1 = 44\) and \(Q_3=63\) into the formula: \(IQR=63 - 44\).

Answer:

19