i = 1 10 ( x i - 5 ) = 5 and i = 1 10 ( x i - 5 ) 2 = 125 , variance of x 1 , x 2 , … , x 10 will be

Question

$\sum_{i = 1}^{10} (x_{i} - 5) = 5$ and $\sum_{i = 1}^{10} {(x_{i} - 5)}^{2} = 125$ , variance of $x_{1}, x_{2}, \dots, x_{10}$ will be

Smart Achievers · Accepted Answer

(3)

$Let x_{i} - 5 = d_{i} σ_{x}^{2}, σ_{d}^{2} = \frac{\sum d_{i}^{2}}{n} - {(\frac{\sum d_{i}}{n})}^{2}$

$= \frac{125}{10} - {(\frac{5}{10})}^{2}$

$= \frac{25}{2} - \frac{1}{4}$

$= \frac{49}{4}$

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