Question

The mean deviation about the median for the data 3, 5, 9,3, 8, 10, 7 is

• A. $\frac 47$
• B. $-\frac 47$
• C. $\frac {16}{7}$
• D. $-\frac {16}{7}$

Answer 1

Answer: (C)

$\frac {16}{7}$

Answer 2

The given data,
$3, 5, 9,3,8,10,7$
Arrange the data in ascending order,
$3,3,5,7,8,9,10$
No. of observations $N= 7$ (Odd)
Then, Median M= $\frac {7+1}{2}= 4$th term = $7$
Now mean deviation about median,
$=\dfrac{∑|x_i−M|}{N}$

$=\frac {|3-7|+|3-7|+|5-7|+|7-7|+|8-7|+|9-7|+|10-7|}{7}$

$=\frac {4+4+2+0+1+2+3}{7}$

$=\frac {16}{7}$

So, the correct option is (C): $\frac {16}{7}$