Question

The mean deviation from the mean $10$ of the data $6,7,10,12,13,\alpha ,12,16$ is

• A. 3.5
• B. 3.25
• C. 3
• D. 3.75

Answer 1

Answer: (B)

Given, $\mathrm{mean}(\bar{x})=10$
$\therefore \mathrm{Mean}(\bar{x})=\frac{6+7+10+12+13+\alpha +12+16}{8}$
$\Rightarrow 10=\frac{76+\alpha }{8}$
$\Rightarrow \alpha =4$
$[|6-10|+|7-10|+|10-10|+|12-10|$
$MD(\bar{x})=\frac{+|13-10|+|4-10|+|12-10|+|16-0|]}{8}$
$MD(\bar{x})=\frac{4+3+0+2+3+6+2+6}{8}$
$MD(\bar{x})=\frac{26}{8}=3.25$
$\therefore$ Mean deviation about mean $=3.25$