A math class has 20 students. In a quiz worth 10 points, 4 students get 6, 7 students get 7, 5 students get 8, 3 students get 9, and 1 student gets 10.
The average of a step function computed with the definite integral matches the average computed in the usual way. Test this in the following situations by finding the average of the values directly, and then as the integral of a step function.