Question

in the data set below, what is the interquartile range? 10 14 18 20 42

Explanation:

Step1: Find the median

The data set is \(10,14,18,20,42\). The median is the middle value. Here, the median \(Q_2 = 18\).

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

For \(Q_1\), consider the lower - half data \(10,14\). The median of this lower - half is \(Q_1=\frac{10 + 14}{2}=12\).
For \(Q_3\), consider the upper - half data \(20,42\). The median of this upper - half is \(Q_3=\frac{20+42}{2}=31\).

Step3: Calculate the inter - quartile range (IQR)

The formula for IQR is \(IQR=Q_3 - Q_1\). Substitute \(Q_1 = 12\) and \(Q_3 = 31\) into the formula: \(IQR=31 - 12\).

Answer:

\(19\)