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

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(C) Let the set of $n$ observations be $x_1, x_2, \dots, x_n$. The mean is given by $\bar{x} = \frac{\sum x_i}{n}$. When each observation $x_i$ is div

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Let the set of $n$ observations be $x_1, x_2, \dots, x_n$. The mean is given by $\bar{x} = \frac{\sum x_i}{n}$. When each observation $x_i$ is divided by $\alpha$ and increased by $10$,the new observations are $y_i = \frac{x_i}{\alpha} + 10$. The new mean $\bar{y}$ is: $\bar{y} = \frac{\sum y_i}{n} = \frac{\sum (\frac{x_i}{\alpha} + 10)}{n}$ $= \frac{1}{\alpha} \cdot \frac{\sum x_i}{n} + \frac{\sum 10}{n}$ $= \frac{1}{\alpha} \cdot \bar{x} + \frac{10n}{n}$ $= \frac{\bar{x}}{\alpha} + 10 = \frac{\bar{x} + 10\alpha}{\alpha}$.

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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