If you take two tests and get a marks out of a maximum b in the first, scoring a/b, and you do better with c marks out of d in the second, scoring c/d , you expect the result of combining the marks for the two tests, the mediant
a+c
b+d
, to lie between the results for the two tests separately.
If 0 < a/b < c/d prove, with reference to the diagram, that
