The mean and standard deviation of 100 items | vedclass

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(A) Given: $n = 100$,$\bar{x} = 50$,and $\sigma = 4$. $1$. Sum of all items $(\Sigma x_i)$: $\bar{x} = \frac{\Sigma x_i}{n}$ $\Rightarrow 50 = \frac{\

Vedclass · Accepted Answer

Sum $= 5000$,Sum of squares $= 251600$

Vedclass · Answer

(A) Given: $n = 100$,$\bar{x} = 50$,and $\sigma = 4$. $1$. Sum of all items $(\Sigma x_i)$: $\bar{x} = \frac{\Sigma x_i}{n}$ $\Rightarrow 50 = \frac{\Sigma x_i}{100}$ $\Rightarrow \Sigma x_i = 5000$. $2$. Sum of squares of items $(\Sigma x_i^2)$: Using the formula $\sigma^2 = \frac{\Sigma x_i^2}{n} - (\bar{x})^2$: $4^2 = \frac{\Sigma x_i^2}{100} - (50)^2$ $16 = \frac{\Sigma x_i^2}{100} - 2500$ $\frac{\Sigma x_i^2}{100} = 2516$ $\Sigma x_i^2 = 251600$.

Marks	$1-3$	$3-5$	$5-7$	$7-9$
Number of students	$40$	$30$	$20$	$10$

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

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