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 original mean is $\bar{X} = \frac{1}{n} \sum_{i=1}^{n} x_{i}$.Let the new observatio

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

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(C) Let $x_{1}, x_{2}, \dots, x_{n}$ be $n$ observations,then the original mean is $\bar{X} = \frac{1}{n} \sum_{i=1}^{n} x_{i}$.Let the new observations be $y_{i} = \frac{x_{i}}{\alpha} + 10$.The new mean $\bar{Y}$ is given by:$\bar{Y} = \frac{1}{n} \sum_{i=1}^{n} y_{i} = \frac{1}{n} \sum_{i=1}^{n} \left( \frac{x_{i}}{\alpha} + 10 \right)$$\bar{Y} = \frac{1}{\alpha} \left( \frac{1}{n} \sum_{i=1}^{n} x_{i} \right) + \frac{1}{n} \sum_{i=1}^{n} 10$$\bar{Y} = \frac{1}{\alpha} \bar{X} + \frac{10n}{n} = \frac{\bar{X}}{\alpha} + 10$Combining the terms,we get $\bar{Y} = \frac{\bar{X} + 10\alpha}{\alpha}$.

$x_i$	$3$	$6$	$9$	$12$
$f_i$	$1$	$2$	$3$	$4$

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

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