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The mean deviation from the mean 10 of the data $6,7,11,12,13, \alpha, 12,16$ is
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Verified Answer
The correct answer is:
3.25
Given, mean $(\bar{x})=10$
$$
\begin{aligned}
& \therefore \operatorname{Mean}(\bar{x})=\frac{6+7+10+12+13+\alpha+12+16}{8} \\
& \Rightarrow \quad 10=\frac{76+\alpha}{8} \\
& \Rightarrow \quad \alpha=4[|6-10|+|7-10|+|10-10|+|12-10| \\
& \operatorname{MD}(\bar{x})=\frac{+|13-10|+|4-10|+|12-10|+|16-0|]}{8} \\
& \operatorname{MD}(\bar{x})=\frac{4+3+0+2+3+6+2+6}{8} \\
& \operatorname{MD}(\bar{x})=\frac{26}{8}=325
\end{aligned}
$$
$\therefore$ Mean deviation about mean $=325$
$$
\begin{aligned}
& \therefore \operatorname{Mean}(\bar{x})=\frac{6+7+10+12+13+\alpha+12+16}{8} \\
& \Rightarrow \quad 10=\frac{76+\alpha}{8} \\
& \Rightarrow \quad \alpha=4[|6-10|+|7-10|+|10-10|+|12-10| \\
& \operatorname{MD}(\bar{x})=\frac{+|13-10|+|4-10|+|12-10|+|16-0|]}{8} \\
& \operatorname{MD}(\bar{x})=\frac{4+3+0+2+3+6+2+6}{8} \\
& \operatorname{MD}(\bar{x})=\frac{26}{8}=325
\end{aligned}
$$
$\therefore$ Mean deviation about mean $=325$
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