Official solution
Here mean = \[\overline x \] = 9
\[ \Rightarrow \] \[\overline x \] = \[{{\sum {{x_i}} } \over n}\] = 9
\[ \Rightarrow \] \[{\sum {{x_i}} }\] = 9 \[ \times \] 5 = 45
Now, standard deviation = 0
\[\therefore\,\,\,\] all the five terms are same i.e.; 9
Now for changed observation
\[{\overline x _{new}}\] = \[{{36 + {x_5}} \over 5} = 10\]
\[ \Rightarrow \] x5 = 14
\[\therefore\,\,\,\] \[\sigma \]new = \[\sqrt {{{\sum {{{\left( {{x_i} - {{\overline x }_{new}}} \right)}^2}} } \over n}} \]
= \[\sqrt {{{4{{\left( {9 - 10} \right)}^2} + {{\left( {14 - 10} \right)}^2}} \over 5}} \] = 2