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If the mean deviation about the median of the numbers $\mathrm{a}, 2 \mathrm{a}, \ldots, 50 \mathrm{a}$ is 50 , then $|\mathrm{a}|$ equals
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4
4
$\frac{1}{\mathrm{n}} \sum\left|\mathrm{x}_{\mathrm{i}}-\mathrm{A}\right|$
$\mathrm{A}=$ Median $=\frac{25 \mathrm{a}+26 \mathrm{a}}{2}=25.5 \mathrm{a}$
Mean deviation $=\frac{1}{50}\{|\mathrm{a}-25.5 \mathrm{a}|+|2 \mathrm{a}-25.5 \mathrm{a}|\}=\frac{2}{50}\{(24.5 \mathrm{a}+23.5 \mathrm{a})+\ldots(0.5 \mathrm{a})\}$
$=\frac{2}{50}\{312.5 \mathrm{a}\}=50 \quad$ (Given)
$\Rightarrow 625 \mathrm{a}=2500 \Rightarrow \mathrm{a}=4$
$\mathrm{A}=$ Median $=\frac{25 \mathrm{a}+26 \mathrm{a}}{2}=25.5 \mathrm{a}$
Mean deviation $=\frac{1}{50}\{|\mathrm{a}-25.5 \mathrm{a}|+|2 \mathrm{a}-25.5 \mathrm{a}|\}=\frac{2}{50}\{(24.5 \mathrm{a}+23.5 \mathrm{a})+\ldots(0.5 \mathrm{a})\}$
$=\frac{2}{50}\{312.5 \mathrm{a}\}=50 \quad$ (Given)
$\Rightarrow 625 \mathrm{a}=2500 \Rightarrow \mathrm{a}=4$
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