Mathematics - Statistics Question with Solution | TestHub

$\overline{x}=\frac{\sum x_i}{n}=9$

$\mathrm{s}.\mathrm{d}=\sqrt{\sum \frac{{\left(x_i-\overline{x}\right)}^2}{n}}=0$

$\Rightarrow x_i=\overline{x}\forall i$

$\therefore$ each term in the original observation is $9$

$\Rightarrow$ observation $1=\{9,9,9,9,9\}$

${\overline{x}}_{\mathrm{new} }=\frac{\sum x_i}{n}=\frac{9+9+9+9+x_5}{5}$

$\Rightarrow 10=\frac{36+x_5}{5}$

$\Rightarrow x_5=14$

$\Rightarrow$ new set of observations $=\{9,9,9,9,14\}$

$\mathrm{s}.{\mathrm{d}}_{\mathrm{new} }=\sqrt{\frac{\sum {\left(x_i-{\overline{x}}_{\mathrm{new}}\right)}^2}{n}}$

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

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

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