JEE Main 2020 (Online) 9th January Morning ShiftQuestion 1
Let the observations $x_i$ ($1\le i\le10$) satisfy the equations, $\sum_{i=1}^{10}(x_i-5)=10$ and $\sum_{i=1}^{10}(x_i-5)^2=40$. If $\mu$ and $\lambda$ are the mean and the variance of the observations, $x_1-3,x_2-3,\ldots,x_{10}-3$, then the ordered pair $(\mu,\lambda)$ is equal to :
Statistics
Solution
$\sum(x_i-5)=10\Rightarrow \bar x-5=1\Rightarrow\bar x=6$. Variance of $x_i-5$ $=\dfrac{40}{10}-1^2=3$, which equals the variance of $x_i$. For $x_i-3$: mean $=3$, variance $=3$. So $(\mu,\lambda)=(3,3)$. Option (D).