Question

what is the difference between the mean and the median of the data set? {22, 8, 10, 18, 12, 20}

Explanation:

Step1: Sort the data set

Sort the data set \(\{22,8,10,18,12,20\}\) in ascending order: \(\{8,10,12,18,20,22\}\)

Step2: Calculate the mean

The mean \(\bar{x}=\frac{8 + 10+12+18+20+22}{6}=\frac{90}{6}=15\)

Step3: Calculate the median

Since there are \(n = 6\) (even number of data points), the median \(M=\frac{\frac{n}{2}\text{th term}+(\frac{n}{2}+1)\text{th term}}{2}=\frac{12 + 18}{2}=15\)

Step4: Find the difference

The difference between the mean and the median is \(|15-15| = 0\)

Answer:

\(0\)