Question

in the data set below, what is the interquartile range? 1 3 4 6 6 7

Explanation:

Step1: Find the median

The data set is \(1,3,4,6,6,7\). The median is \(\frac{4 + 6}{2}=5\).

Step2: Split the data into lower and upper halves

Lower - half: \(1,3,4\); Upper - half: \(6,6,7\)

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

For the lower - half \(1,3,4\), \(Q_1 = 3\). For the upper - half \(6,6,7\), \(Q_3=6\)

Step4: Calculate the inter - quartile range (IQR)

\(IQR=Q_3 - Q_1\)
\(IQR = 6-3\)

Answer:

\(3\)