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