Question

The mean deviation of the data $2,9,9,3,6,9,4$ from the mean is

• A. 2.23
• B. 3.23
• C. 2.57
• D. 3.57
• E. 1.03

Answer 1

Answer: (C)

Mean of the given data is
$\bar{x}=\frac{2+9+9+3+6+9+4}{7}=\frac{42}{7}=6$
The deviations of the respective observations from the mean $\bar{x}$, i.e. $x_i-\bar{x}$ are
$2-6,9-6,9-6,3-6,6-6,9-6,4-6$
$\Rightarrow -4,3,3,-3,0,3,-2$
The absolute values of the deviations, i.e. $\left|x_i-\bar{x}\right|$ are $4,3,3,3,0,3,2$.
The required mean deviation about the mean is
$MD(\bar{x})=\frac{\sum _{i=1}^7\left|x_i-\bar{x}\right|}{7}$
$=\frac{4+3+3+3+0+3+2}{7}$
$=\frac{18}{7}=2.57$