Question Number 215418 by BaliramKumar last updated on 06/Jan/25
Answered by TonyCWX08 last updated on 06/Jan/25
$${Let} \\ $$$${Sum}\:{of}\:{correct}\:{numbers}={x} \\ $$$${Sum}\:{of}\:{square}\:{of}\:{correct}\:{numbers}={y} \\ $$$$ \\ $$$$\frac{{x}+\mathrm{10}}{\mathrm{25}}=\mathrm{42} \\ $$$${x}=\mathrm{42}\left(\mathrm{25}\right)−\mathrm{10}=\mathrm{1040} \\ $$$$ \\ $$$$\sqrt{\frac{{y}+\mathrm{10}^{\mathrm{2}} }{\mathrm{25}}−\mathrm{42}^{\mathrm{2}} }=\mathrm{5}\Rightarrow{y}=\mathrm{44625} \\ $$$$ \\ $$$${New}\:{mean} \\ $$$$=\frac{\mathrm{1040}+\mathrm{210}}{\mathrm{25}}=\mathrm{50} \\ $$$$ \\ $$$${New}\:{S}.{D} \\ $$$$=\sqrt{\frac{\mathrm{44625}+\mathrm{210}^{\mathrm{2}} }{\mathrm{25}}−\mathrm{50}^{\mathrm{2}} }=\sqrt{\mathrm{1049}} \\ $$
Commented by BaliramKumar last updated on 06/Jan/25
$${thanks} \\ $$