Question

Find the mean deviation about the median for the following data: $3,9,5,3,12,10,18,4,7,19,21.$

Answer 1

Given data: $3,9,5,3,12,10,18,4,7,19,21.$

Arranging the given data in ascending order: $3,3,4,5,7,9,10,12,18,19,21$

Total number of terms is 11 which is odd.
So, Median $\left(M\right)={\left(\frac{(11+1)}{2}\right)}^{th}$ term

$\Rightarrow M=6^{th}$ observation which is equal to $9$.

$\therefore M=9$

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

Median, $M=9$

Mean deviation about median $=\frac{1}{n}\sum |x_i-M|$

$M.D.\left(M\right)=\frac{\left(\begin{array}{c}|3-9|+|3-9|+|4-9|+|5-9|+|7-9|+|9-9|\\ +|10-9|+|12-9|+|18-9|+|19-9|+|21-9|\end{array}\right)}{11}$

$=\frac{\left(\begin{array}{c}|-6|+|-6|+|-5|+|-4|+|-2|+|0|\\ +|1|+|3|+|9|+|10|+|12|\end{array}\right)}{11}$

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

$=\frac{\left(58\right)}{11}$

$=5.27$