Question

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

• A. $5.27$
• B. $6.29$
• C. $4.27$
• D. $3.29$

Answer 1

Answer: (A)

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 $= \left(\frac{11+1}{2}\right)^{th}$ observation or $6^{th}$ 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 $\sum\limits^{11}_{i = 1} \left|x_{i}-M\right| = 58$
and $M.D. \left(M\right) = \frac{1}{11}\sum\limits^{11}_{i = 1} \left|x_{i}-M\right|$
$= \frac{1}{11}\times58 = 5.27$