The mean of the data: $2, 8, 6, 5, 4, 5, 6, 3, 6, 4, 9, 1, 5, 6, 5$ is given to be $5$. Based on this information,is it correct to say that the mean of the data: $10, 12, 10, 2, 18, 8, 12, 6, 12, 10, 8, 10, 12, 16, 4$ is $10$? Give reason.
(A) Yes,it is correct.
Let the first set of data be $x_i$. The mean is given as $\bar{x} = 5$.
The second set of data is $y_i = 2x_i$.
According to the properties of the mean,if each observation in a data set is multiplied by a constant $k$,the new mean becomes $k$ times the original mean.
Here,$k = 2$.
Therefore,the new mean = $2 \times 5 = 10$.
Thus,the statement is correct.
Let the first set of data be $x_i$. The mean is given as $\bar{x} = 5$.
The second set of data is $y_i = 2x_i$.
According to the properties of the mean,if each observation in a data set is multiplied by a constant $k$,the new mean becomes $k$ times the original mean.
Here,$k = 2$.
Therefore,the new mean = $2 \times 5 = 10$.
Thus,the statement is correct.
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