Question

find the median of the data set: 18, 19, 17, 14, 20, 20, 15, 21

Explanation:

Step1: Sort the data set

Sort the data set \(18, 19, 17, 14, 20, 20, 15, 21\) in ascending order: \(14, 15, 17, 18, 19, 20, 20, 21\).

Step2: Find the median

Since there are \(n = 8\) (even number of data points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values.
\(\frac{n}{2}=\frac{8}{2} = 4\) and \(\frac{n}{2}+1=4 + 1=5\).
The \(4\)th value is \(18\) and the \(5\)th value is \(19\).
Median \(=\frac{18 + 19}{2}=\frac{37}{2}=18.5\).

Answer:

\(18.5\)