Mean and standard deviation of 100 items are | vedclass

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Question

Here, $\bar{x}=50, n=100$ and $\sigma=4$

$	herefore \quad \frac{\Sigma x_{i}}{100}=50$

$\Rightarrow \quad \Sigma x_{i}=5000$

$	ext { and }

Vedclass · Accepted Answer

Vedclass · Answer

Here, $\bar{x}=50, n=100$ and $\sigma=4$

$	herefore \quad \frac{\Sigma x_{i}}{100}=50$

$\Rightarrow \quad \Sigma x_{i}=5000$

$	ext { and } \sigma^{2}=\frac{\Sigma f_{i} x_{i}^{2}}{\Sigma f_{i}}-\left(\frac{\Sigma f_{i} x_{i}}{\Sigma f_{i}}ight)^{2}$

$\Rightarrow \quad (4)^{2}=\frac{\Sigma f_{i} x_{i}^{2}}{100}-(50)^{2}$

$\Rightarrow \quad 16=\frac{\Sigma f_{i} x_{i}^{2}}{100}-2500$

$\Rightarrow \frac{\Sigma f_{i} x_{i}^{2}}{100}=16+2500=2516$

$\Sigma f_{i} x_{i}^{2}=251600$

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

Mean and standard deviation of 100 items are 50 and $4,$ respectively. Then find the sum of all the item and the sum of the squares of the items.

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