Question

in the data set below, what is the interquartile range? 26 58 70 73 79

Explanation:

Step1: Find the median

The data set is \(26,58,70,73,79\). The median (second - quartile \(Q_2\)) is the middle value. Since there are \(n = 5\) values, the median is the third value. So \(Q_2=70\).

Step2: Find the lower half and upper half

The lower half of the data is \(26,58\). The median of the lower half (first - quartile \(Q_1\)) is \(\frac{26 + 58}{2}=\frac{84}{2}=42\).
The upper half of the data is \(73,79\). The median of the upper half (third - quartile \(Q_3\)) is \(\frac{73+79}{2}=\frac{152}{2}=76\).

Step3: Calculate the inter - quartile range (IQR)

The formula for the inter - quartile range is \(IQR=Q_3 - Q_1\). Substitute \(Q_1 = 42\) and \(Q_3=76\) into the formula. So \(IQR=76 - 42=34\).

Answer:

\(34\)