If $\displaystyle \sum_{i =1}^{10} (x_1 - 15) = 12$ and $\displaystyle \sum_{i = 1}^{10} (x_i - 15)^2 = 18$, then the S.D. of observations $x_1, x_2 ............. x_{10}$ is

Using the properties of standard deviation, the standard deviation of the observations $x_i$ equals the standard deviation of $(x_i - 15)$ because adding or subtracting a constant does not change the spread. The variance is calculated as the average of the squared deviations, giving $18 / 10 = 1.8$. The standard deviation is the square root of $1.8$, which equals $3 / 5$. The standard deviation is 3/5.

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