If ∑ _ i = 1 ^ 9 ( x _ i - 5) = 9 and ∑ _ i = 1 ^ 9 ( x _ i - 5) ^...

Given $\mathop{∑}_{i = 1}^{9} {x}_{i} - 45 = 9$

$⇒ \mathop{∑}_{i = 1}^{9}{x}_{i} = 54$

Also $\mathop{∑}_{i = 1}^{9}\left({x}_{i}^{2} - 10{x}_{i} + 25\right) = 45$

$⇒ \mathop{∑}_{i = 1}^{9}{x}_{i}^{2} - 10 \times 54 + 25 \times 9 = 45$

$⇒ ∑ {x}_{i}^{2} = 45 + 540 - 225$

$= 360$
$∴ {\sigma}^{2} = \dfrac{∑ {x}_{i}^{2}}{N} - {\left(\dfrac{∑ {x}_{i}}{N}\right)}^{2}$

$= \dfrac{360}{9} - {( \dfrac{54}{9} )}^{2}$

So, variance $= 40 - 36 = 4$

$∴ SD = 2$