Question

in the data set below, what is the interquartile range? 20 24 28 34 45 50 60 75 81 87 93 93

Explanation:

Step1: Find the median

The data set has \(n = 12\) values. The median is the average of the \(6^{th}\) and \(7^{th}\) values.
The \(6^{th}\) value is \(50\) and the \(7^{th}\) value is \(60\). So the median \(Q_2=\frac{50 + 60}{2}=55\).

Step2: Find \(Q_1\)

The lower - half of the data is \(20,24,28,34,45,50\). Since \(n = 6\) (even), \(Q_1=\frac{28+34}{2}=31\).

Step3: Find \(Q_3\)

The upper - half of the data is \(60,75,81,87,93,93\). Since \(n = 6\) (even), \(Q_3=\frac{81 + 87}{2}=84\).

Step4: Calculate the inter - quartile range (IQR)

The formula for \(IQR\) is \(IQR=Q_3 - Q_1\).
Substitute \(Q_1 = 31\) and \(Q_3=84\) into the formula: \(IQR=84 - 31=53\).

Answer:

\(53\)