Question

Find the mean deviation about the median for the following data.
$13,17,16,11,13,10,16,11,18,12,17$

Answer 1

Total number of observations = $11$

When arranged in ascending order, as shown: $10,11,11,12,13,13,16,16,17,17,18$, the middle number is $13$ and hence the median is $13$.

The mean deviation about the median is given by

$=\frac{(13-10)+2(13-11)+(13-12)+2(13-13)+2(13-16)+2(13-17)+(13-18)}{11}$

$=\frac{3+2\left(2\right)+1+2\left(0\right)+2(-3)+2(-4)+(-5)}{11}$

$=\frac{-11}{11}$

$=-1$