Mean of n numbers X1, X2,--------Xn is m. If Xn is replaced by x the new mean is
To find the new mean when Xn is replaced by x, we need to take into account the total sum of the n numbers and the number of elements (n) in the dataset.
Let's denote the original sum of the n numbers as S. Then, the original mean (m) can be calculated as S/n.
When Xn is replaced by x, the new sum of the numbers can be obtained by subtracting Xn from the original sum (S) and then adding x. So, the new sum (S') can be calculated as S - Xn + x.
The new mean (m') can be calculated by dividing the new sum (S') by the number of elements (n). Thus, m' = (S'/(n-1)).
Therefore, the new mean (m') when Xn is replaced by x is (S - Xn + x)/(n-1).