The mean of a set of observations is bar{x}. | vedclass

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

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

Vedclass · Answer

(C) Let the $n$ observations be $x_1, x_2, \dots, x_n$. 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 new mean $\bar{y}$ is: $\bar{y} = \frac{1}{n} \sum_{i=1}^{n} \left( \frac{x_i}{\alpha} + 10 \right)$ $= \frac{1}{\alpha} \left( \frac{1}{n} \sum_{i=1}^{n} x_i \right) + \frac{1}{n} (10n)$ $= \frac{\bar{x}}{\alpha} + 10$ $= \frac{\bar{x} + 10\alpha}{\alpha}$.

The mean of a set of observations is $\bar{x}$. If each observation is divided by $\alpha$ $(\alpha \neq 0)$ and then increased by $10$,what is the mean of the new set?

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