The mean of five observations is M. If each observation is divided by 2,then what is the new set of observations?

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$$\begin{gathered} Let the set of observations be x_1, x_2, ..., x_n. \\ Then, mean of these observations = \frac{Sum of all observations}{Number of observations} = \frac{x_1 + x_2 + ... + x_n}{n} = M ...\left(i\right) \\ Now, dividing each observation by 2, the new set of observations is \frac{x_1}{2}, \frac{x_2}{2}, ..., \frac{x_n}{2}. \\ Then, Sum of all new observations = \frac{x_1}{2} + \frac{x_2}{2} + ... + \frac{x_n}{2} = \frac{1}{2}\left(x_1 + x_2 + ... + x_n\right) \\ Therefore, new mean = \frac{Sum of all new observations}{Number of observations} = \frac{\frac{1}{2}\left(x_1 + x_2 + ... + x_n\right)}{n} = \frac{1}{2} \times \frac{x_1 + x_2 + ... + x_n}{n} = \frac{1}{2}M [From \left(i\right)] \\ NOTE: Since, the question is unclear, it is assumed in the above solution that the new mean is required to be calculated. \end{gathered}$$

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