If the mean and the sum of squares of 10 observations are 40 and 16160 respectively, then what is the standard deviation?

Explanation

The variance is given by \sigma^2 = \frac{\sum x_i^2}{n} - (\overline{X})^2. Substituting the given values: \sigma^2 = \frac{16160}{10} - (40)^2 = 1616 - 1600 = 16. The standard deviation is \sigma = \sqrt{16} = 4.

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