What does the author achieve by mixing exact and approximate number in ‘ a contribution to statistics? ”

Interpreting poetry is subjective: so this effect might be different on different people and my answer might be different from yours. 

i think that the approximate and non-approximate numbers correspond to our efforts to measure and capture life (the exact) but we often fail because the world is not always as we want it to be (but often it's messy and fuzzy and not crearly structured, and even cruel: "c ruel /when forced by circumstances /— better not to know -)
the only thing that is certain - and it has an exact number - is death. 
so i think it's a play on our need for certainty in live and a difficulty of achieving it, apart from death.