The mean and standard deviation of 100 items | vedclass

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Question

(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 $\sigma^2 = \frac{\Sigma x_i^2}{n} - (\bar{x})^2$: $4^2 = \frac{\Sigma x_i^2}{100} - (50)^2$ $16 = \frac{\Sigma x_i^2}{100} - 2500$ $\frac{\Sigma x_i^2}{100} = 2516$ $\Sigma x_i^2 = 251600$.

Class Interval	Frequency
$0 - 6$	$10$
$6 - 12$	$8$
$12 - 18$	$6$
$18 - 24$	$4$
$24 - 30$	$2$

Class	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
$f_i$	$3$	$7$	$12$	$15$	$8$	$3$	$2$

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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The variance of the following frequency distribution is
Class Interval Frequency
$0 - 6$ $10$
$6 - 12$ $8$
$12 - 18$ $6$
$18 - 24$ $4$
$24 - 30$ $2$

Calculate the mean,variance,and standard deviation for the following distribution:

Class $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$

$f_i$ $3$ $7$ $12$ $15$ $8$ $3$ $2$

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