The arithmetic mean of a set of observations | vedclass

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Question

(C) Let $x_1, x_2, \dots, x_n$ be $n$ observations,then the mean is given by $\bar{X} = \frac{1}{n} \sum_{i=1}^{n} x_i$.Let the new observations be $y

Vedclass · Accepted Answer

$\frac{\bar{X} + 10\alpha}{\alpha}$

Vedclass · Answer

(C) Let $x_1, x_2, \dots, x_n$ be $n$ observations,then the mean is given by $\bar{X} = \frac{1}{n} \sum_{i=1}^{n} x_i$.Let the new observations be $y_i = \frac{x_i}{\alpha} + 10$.The mean of the new series $\bar{Y}$ is given by:$\bar{Y} = \frac{1}{n} \sum_{i=1}^{n} \left( \frac{x_i}{\alpha} + 10 \right)$$\bar{Y} = \frac{1}{\alpha} \left( \frac{1}{n} \sum_{i=1}^{n} x_i \right) + \frac{1}{n} (10n)$$\bar{Y} = \frac{\bar{X}}{\alpha} + 10$$\bar{Y} = \frac{\bar{X} + 10\alpha}{\alpha}$

The arithmetic mean of a set of observations is $\bar{X}$. If each observation is divided by $\alpha$ and then increased by $10$,then the mean of the new series is:

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