Question

The mean deviation about the median of the following set of observations $3,9,5,3,12,10,18,4,7,19,21$ is 58/k then k=

Answer 1

Arranging data in ascending order,

$3,3,4,5,7,9,10,12,18,19,21$

$\Rightarrow$ Number of observation $\left(n\right)=11$ (odd)

$Median={\left(\frac{11+1}{2}\right)}^{th}obs=6^{th}obs$

$\therefore$ $Median\left(M\right)=9$

Now, we calculate mean deviation about median

$M.D.\left(M\right)=\frac{\sum |x_i-M|}{11}$

$=\frac{|3-9|+|3-9|+|4-9|+|5-9|+|7-9|+|9-9|+|10-9|+|12-9|+|18-9|+|19-9|+|21-9|}{11}$

$=\frac{6+6+5+4+2+0+1+3+9+10+12}{11}$

$=\frac{58}{11}$

$k=11$