The mean and standard deviation of 100 items | vedclass

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Question

(C) Given: $n = 100$,$\bar{x} = 50$,and $\sigma = 4$. The formula for standard deviation is $\sigma = \sqrt{\frac{\sum x_i^2}{n} - (\bar{x})^2}$. Subs

Vedclass · Accepted Answer

$251600$

Vedclass · Answer

(C) Given: $n = 100$,$\bar{x} = 50$,and $\sigma = 4$. The formula for standard deviation is $\sigma = \sqrt{\frac{\sum x_i^2}{n} - (\bar{x})^2}$. Substituting the given values: $4 = \sqrt{\frac{\sum x_i^2}{100} - (50)^2}$ Squaring both sides: $16 = \frac{\sum x_i^2}{100} - 2500$ $\frac{\sum x_i^2}{100} = 2500 + 16 = 2516$ $\sum x_i^2 = 2516 	imes 100 = 251600$. Thus,the sum of the squares of all items is $251600$.

The mean and standard deviation of $100$ items are $50$ and $4$ respectively. The sum of the squares of all the items is:

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