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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.

  • Did you try to express the new variance and make it equal to the previous expression of variance? – Botond Apr 01 '19 at 06:35
  • Refer to this question: https://math.stackexchange.com/questions/2837813/sample-variance-recursive-relation-n-s-n12-n-1s-n2-big-fracnn/2837838#2837838 – heropup Apr 01 '19 at 06:50

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