1. suppose we only have 3 (odd) number of values x1,x2, x3 ordered already
so the median is x2.
The new sequence will be x1-x2, 0, x3-x2.
We see the new median is 0.
2. suppose we have 4 (even) number of values y1, y2, y3, y4, ordered already.
the median is (y2+y3)/2.
The new sequence is : y1-(y2+y3)/2, y2-(y2+y3)/2, y3-(y2+y3)/2, y4-(y2+y3)/2.
The new median is: (y2-(y2+y3)/2+ y3-(y2+y3)/2) which is also 0.
This observation is useful when we estimate the shift estimator of a Sign Scores test.
