The mean and the standard deviation (S . D .) of five observations...

$\overset{¯}{x} = \dfrac{∑ {x}_{i}}{n} = 9$

$s . d = \sqrt{∑ \dfrac{{\left({x}_{i} - \overset{¯}{x}\right)}^{2}}{n}} = 0$

$⇒ {x}_{i} = \overset{¯}{x} \forall i$

$∴$ each term in the original observation is $9$

$⇒$ observation $1 = { 9, 9, 9, 9, 9 }$

$\overset{¯}{x}new = \dfrac{∑ {x}_{i}}{n} = \dfrac{9 + 9 + 9 + 9 + {x}_{5}}{5}$

$⇒ 10 = \dfrac{36 + {x}_{5}}{5}$

$⇒ {x}_{5} = 14$

$⇒$ new set of observations $= { 9, 9, 9, 9, 14 }$

$s . {d}_{new} = \sqrt{\dfrac{∑ {\left({x}_{i} - \overset{¯}{x}new\right)}^{2}}{n}}$

$= \sqrt{\dfrac{( 9 - 10{)}^{2} + ( 9 - 10{)}^{2} + ( 9 - 10{)}^{2} + ( 14 - 10{)}^{2}}{5}}$

$= \sqrt{\dfrac{4 + {4}^{2}}{5}}$

$= \sqrt{\dfrac{20}{5}} = 2$