How does a change in number affect the mean or median?

Answer 1

Mean

Suppose there are n numbers whose mean is m. If one of the numbers changes from x to y then the mean changes to m + (y-x)/n

Another way to see this is to express the new mean as m - x/n + y/n: take the old mean, remove the contribution than was made by x and replace it with the contribution made by y.

Median

If n is odd, then a change in any number other than the (n+1)/2 th number in the ordered sequence will make no difference to the median.

If the (n+1)/2 th number changes, but still remains in the same position, then its new value will be the new median.

If the (n+1)/2 th number becomes larger than the next number, then that next number becomes the new median. Similarly, if it becomes smaller than the number before it then that number becomes the new median.

The situation is similar if there are an even number of values except that changes in either of the two middle numbers can affect the median.