Mathematics - Statistics Question with Solution | TestHub

Mean $=\frac{x_1+x_2+x_3+\dots \dots +x_{19}+25}{20}=10$$\Rightarrow x_1+x_2+x_3+\dots \dots \dots +{\mathrm{x}}_{19}+25=200$

$\Rightarrow x_1+x_2+x_3+\dots \dots \dots +x_{19}=175$

New mean $=\frac{x_1+x_2+x_3+\dots \dots +x_{19}+35}{20}=\frac{175+35}{20}=10.5$

S.D. $=\sqrt{\frac{x_1^2+x_2^2+x_3^2+\dots \dots +x_{19}^2+(25{)}^2}{20}-(10{)}^2}$

$\Rightarrow 2.5=\sqrt{\frac{x_1^2+x_2^2+x_3^2+\dots \dots +x_{19}^2+(25{)}^2}{20}-(10{)}^2}$

$\Rightarrow {\mathrm{x}}_1^2+{\mathrm{x}}_2^2+{\mathrm{x}}_3^2+\dots \dots +{\mathrm{x}}_{19}^2=1500$

New $\mathrm{S}.\mathrm{D}. =\sqrt{\frac{x_1^2+x_2^2+x_3^2+\dots \dots +x_{19}^2+(35{)}^2}{20}-(10.5{)}^2}$

$=\sqrt{\frac{1500+(35{)}^2}{20}-(110.25)}$

$=\sqrt{26}$

$(\alpha ,\beta )=(10.5,26)$