Question

in the data set below, what is the interquartile range? 2 8 2 3 6 7 1

Explanation:

Step1: Sort the data set

Sort the data set \(1,2,2,3,6,7,8\).

Step2: Find the median

The median \(Q_2\) of the data set (since \(n = 7\), the median is the \(\frac{7 + 1}{2}=4^{th}\) value). So \(Q_2=3\).

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

For the lower half of the data \(1,2,2\) ( \(n_1=3\)), the median \(Q_1\) (the \(\frac{3 + 1}{2}=2^{nd}\) value) is \(2\).
For the upper half of the data \(6,7,8\) ( \(n_2 = 3\)), the median \(Q_3\) (the \(\frac{3+1}{2}=2^{nd}\) value) is \(7\).

Step4: Calculate the inter - quartile range

The inter - quartile range \(IQR=Q_3 - Q_1\). Substitute \(Q_1 = 2\) and \(Q_3=7\) into the formula: \(IQR=7 - 2\).

Answer:

\(5\)