JEE Main 2021 (Online) 16th March Morning ShiftQuestion 1
Consider three observations $a$, $b$ and $c$ such that $b=a+c$. If the standard deviation of $a+2$, $b+2$, $c+2$ is $d$, then which of the following is true ?
Statistics
Solution
Standard deviation is unchanged by adding $2$, so $d^2=\frac{a^2+b^2+c^2}{3}-\left(\frac{a+b+c}{3}\right)^2$ with $a+c=b$: $9d^2=3(a^2+b^2+c^2)-4b^2=3(a^2+c^2)-b^2$. So $b^2=3(a^2+c^2)-9d^2$.