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  4. The mean deviation from the mean 10 of the data 6,7,10,12,13, α , 12,16 is

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

TS EAMCET 2017

Solution:

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