Question

in the data set below, what is the interquartile range?
49 52 34 19 35 49 54 41 35 25

Explanation:

Step1: Sort the data

Sort the data set \(19,25,34,35,35,41,49,49,52,54\)

Step2: Find the median

Since there are \(n = 10\) data points, the median is the average of the \(5^{th}\) and \(6^{th}\) values. The median \(Q_2=\frac{35 + 41}{2}=38\)

Step3: Find \(Q_1\)

The lower half of the data is \(19,25,34,35,35\). The median of the lower half (\(Q_1\)) is the \(3^{rd}\) value. So \(Q_1 = 34\)

Step4: Find \(Q_3\)

The upper half of the data is \(41,49,49,52,54\). The median of the upper half (\(Q_3\)) is the \(3^{rd}\) value. So \(Q_3=49\)

Step5: Calculate the inter - quartile range (IQR)

The formula for \(IQR\) is \(IQR=Q_3 - Q_1\). Substitute \(Q_1 = 34\) and \(Q_3 = 49\) into the formula: \(IQR=49-34\)

Answer:

\(15\)