Question

in the data set below, what is the interquartile range? 32 42 44 62 84

Explanation:

Step1: Find the median

The data set is \(32,42,44,62,84\). The median (middle value) is \(44\).

Step2: Split the data into lower and upper halves

Lower - half: \(32,42\); Upper - half: \(62,84\)

Step3: Find \(Q_1\) (median of lower - half)

For \(32,42\), \(Q_1=\frac{32 + 42}{2}=\frac{74}{2}=37\)

Step4: Find \(Q_3\) (median of upper - half)

For \(62,84\), \(Q_3=\frac{62+84}{2}=\frac{146}{2}=73\)

Step5: Calculate the inter - quartile range (IQR)

\(IQR = Q_3-Q_1\)
\(IQR=73 - 37\)

Answer:

\(36\)