If the mean of \( \mathrm{n} \) observations \( \mathrm{ax}_{1}, \mathrm{ax}_{2}, \mathrm{ax}_{3...

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If the mean of \( \mathrm{n} \) observations \( \mathrm{ax}_{1}, \mathrm{ax}_{2}, \mathrm{ax}_{3}, \ldots, \mathrm{ax}_{\mathrm{n}} \) is
a \( \overline{\mathrm{X}} \), show that
\[
\left(a x_{1}-a \bar{X}\right)+\left(a x_{2}-a \bar{X}\right)+\ldots .+\left(a_{n}-a \bar{X}\right)=0
\]
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