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Answer 1

Answer:

${ \boxed{\bf {\red{ | \beta - \alpha | = 0}}}}$

Step-by-step explanation:

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$\sf \: Let \: \: \: \alpha = \beta$

°•° Standard deviations remain unchanged if observation are added or subtracted by a fixed number .

$\therefore \rm \pink{ standard \: \: deviation\: = \sqrt{ \frac{ { \sum}^{18}_{i = 1}(x _i { - \alpha )}^{2} }{18} - { \bigg[ \sqrt{ \frac{ { \sum}^{18}_{i = 1}(x _i - \alpha ) }{18} \bigg]}^{2} }}}$

$\qquad: \implies\rm { standard \: \: deviation\: = \sqrt{( \frac{90}{18} - {( \frac{36}{18} })^{2} } = 1} \: \: which \: is \: given \:$

$\boxed{ \tt{ \green{Hence \: \: \alpha = \beta \: \: according \: \: to \: \: the \: \: conditions \: }}}$

$\huge{ \underline{ \boxed{ \rm{ \orange{ \therefore \: | \beta - \alpha | = 0}}}}} \: \: \bigstar$

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Hope it will help you Fradu >3

Answer 2

$\huge\red{\underline{\underline{\bf Answer}}}$

Let α=β

°•° Standard deviations remain unchanged if observation are added or subtracted by a fixed number .

$\begin{gathered} \therefore \rm \pink{ standard \: \: deviation\: = \sqrt{ \frac{ { \sum}^{18}_{i = 1}(x _i { - \alpha )}^{2} }{18} - { \bigg[ \sqrt{ \frac{ { \sum}^{18}_{i = 1}(x _i - \alpha ) }{18} \bigg]}^{2} }}} \\ \\ \end{gathered}$

$\qquad: \implies\rm { standard \: \: deviation\: = \sqrt{( \frac{90}{18} - {( \frac{36}{18} })^{2} } = 1} \: \: which \: is \: given$

$\huge{ \underline{ \boxed{ \rm{ \orange{ \therefore \: | \beta - \alpha | = 0}}}}}$

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