I'm not sure you can use the Mean Value Theorem for Integrals to find the average value when the function is not continuous on a closed interval.

The mutation function is

This function of course is not continuous on the end points; a requirement of the Mean Value Theorem.

Note I can still formulate the expression:

If I integrate this, I get:

Then

Since

Note when that comes out to be approx 0.138.

Bram, I'm not sure. I've never applied the Mean Value Theorem to a function non-continuous on a closed interval. However, after looking as it a while, seems to me the concept is still valid if one interprets the theorem as the value of the function which when multiplied by the length of the interval, gives the integral over that interval. Perhaps that interpretation is not valid though. Maybe someone more knowledgeable in analysis can comment further about this.