Question

Find the mean deviation about the median for the data
$13,17,16,14,11,13,10,16,11,18,12,17$

Answer 1

Given: 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 19

n = 12

median = $\frac{6^{th}obs+7^{th}obs}{2}$

$=\frac{13+14}{2}=\frac{27}{2}=13.5$

mean deviation about median

=$\frac{(110-13.51+\mathrm{111.13.51}+111-13.51+112-13.51+113-13.51+113-13.51+114-13.51+116-13.5+116-13.51+117-13.51+117-13.51+118-13.51)}{12}$

=$\frac{3.5+2.5+2.5+1.5+0.5+0.5+0.5+2.5+2.5+3.5+3.5+4.5}{12}$

$=\frac{28}{12}=2.23$