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Let $\bar{x}$ be the mean of $x_{1}, x_{2}, x_{3}, \ldots ., x_{n} .$ If $x_{i}=a+c y_{i}$ for some constants a and $\mathrm{c}$, then what will be the mear $\mathrm{y}_{2}, \mathrm{y}_{3}, \ldots, \mathrm{y}_{\mathrm{n}}$
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The correct answer is:
$\underline{\mathrm{X}-}$
Given, Mean of $x_{i}=\bar{x}$ Also, Given $x_{i}=a+c y_{i}$ Mean of $\mathrm{a}+\mathrm{cy}_{\mathrm{i}}=\overline{\mathrm{x}}$
$\Rightarrow$ Mean of $\mathrm{cy}_{\mathrm{i}}=\overline{\mathrm{x}}-\mathrm{a}$
$\Rightarrow$ Mean of $y_{i}=\frac{\bar{x}-a}{c}$
$\Rightarrow$ Mean of $\mathrm{cy}_{\mathrm{i}}=\overline{\mathrm{x}}-\mathrm{a}$
$\Rightarrow$ Mean of $y_{i}=\frac{\bar{x}-a}{c}$
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