Q.Find the mean deviation about the median for the data: $6, 9, 3, 15, 12, 8, 10, 5$.

[!TLDR] With even $n=8$, the median is the average of the two middle sorted values. [!ANSWER] Median $ …

Sorting the data $6,9,3,15,12,8,10,5$ gives $3,5,6,8,9,10,12,15$. Since $n=8$ is even, the median is the average of the 4th and 5th values: $M=\dfrac{8+9}{2}=8.5$. The absolute deviations from $M=8.5$, in sorted order, are: $|3-8.5|=5.5$, $|5-8.5|=3.5$, $|6-8.5|=2.5$, $|8-8.5|=0.5$, $|9-8.5|=0.5$, $|10-8.5|=1.5$, $|12-8.5|=3.5$, $|15-8.5|=6.5$. …

Sort the data; for even $n$, average the two middle values to get the median $M$; form $|x_i-M|$ for …

A common mistake for even $n$ is picking just one of the two middle sorted values as the me …