Consider a set of $n$ observations {$x_1,...x_n$}, with mean $\bar{x}$ and variance $s^2$.When a new observation $x_{n+1}$ is added to this set,the mean decreases,but the variance remains the same.Express $x_{n+1}$ in terms of $n,\bar{x},s^2$.

I can see that $x_{n+1}$ should lie below $\bar{x}$ but I cannot work with the equal variance criteria.


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