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Q.
Mean deviation about the median for the data 3,9 , $5,3,12,10,18,4,7,19,21$ is
Statistics
Solution:
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, $\displaystyle\sum_{i=1}^{11}\left|x_i-M\right|=58$
and
$\operatorname{MD}(M) =\frac{1}{11} \displaystyle\sum_{i=1}^{11}\left|x_i-M\right| $
$=\frac{1}{11} \times 58=5.27$