Question

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

• A. 6.53
• B. 5.27
• C. 10.56
• D. 12.96

Answer 1

The correct option is B 5.27

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