Question

Mean deviation about the median for the data 3,9 , $5,3,12,10,18,4,7,19,21$ is

• A. $4.27$
• B. $5.24$
• C. $5.27$
• D. $4.24$

Answer 1

Answer: (C)

Here, the number of observations is 11 which is odd. Arranging the data into ascending order we have $3,3,4,5$, $7,9,10,12,18,19,21$.
Now, median $={\left(\frac{11+1}{2}\right)}^{\text{th }}$ or $6^{\text{th }}$ observation $=9$
The absolute values of the respective deviations from the median, i.e., $\left|x_i-M\right|$ are $6,6,5,4,2,0,1,3,9,10,12$.
Therefore, $\sum _{i=1}^{11}\left|x_i-M\right|=58$
and
$\mathrm{MD}(M)=\frac{1}{11}\sum _{i=1}^{11}\left|x_i-M\right|$
$=\frac{1}{11}\times 58=5.27$