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Previous Year Question (PYQs)

The mean of 100 observations is 50 and their standard deviation is 5. The sum of squares of all observations is —




Solution

Let $\bar{x} = 50$, $\sigma = 5$, and $n = 100.$ We know, $\sigma^2 = \dfrac{\sum x^2}{n} - \bar{x}^2$ $\Rightarrow \sum x^2 = n(\sigma^2 + \bar{x}^2)$ $= 100(5^2 + 50^2) = 100(25 + 2500) = 100 \times 2525 = 2,52,500.$

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