The mean deviation about the median for the following data $6,3,4,9,2,7$ and 11 is
The mean deviation about the median for the following data $6,3,4,9,2,7$ and 11 is
$1.89$
$2.57$
$3.14$
$6.23$
Solution
Given data is 6, 3, 4, 9,2,7 and 11
There are total 7 observation which isodd.
So, Median $=$
$\left(\frac{\mathrm{x}-1}{2}\right)^{\mathrm{th}}=\left(\frac{\mathrm{x}+1}{2}\right)^{\mathrm{th}}=\frac{8^{\mathrm{th}}}{2}=4^{\text {th }}$
Observation are $2,3,4,6,7,9,11$
So, Medium $=6=\mathrm{M}$
Mean derivation about Median $=$
$\frac{1}{x} \sum_{1-1}^x\left|x_i-M\right|$
$\frac{1}{7}\left[\begin{array}{l}|12-6|+|3-6|+|4-6| \\ +|6-6|+|7-6|+|9-6|+|11-6|\end{array}\right]$
$\begin{aligned} & \frac{1}{7}[|-4|+|-3|+|-2|+0+|1|+|3|+|5|] \\ & \frac{1}{7}[4+3+2+1+3+5]=\frac{18}{7}=2.57\end{aligned}$