- Location
- Lockport, IL
- Occupation
- Retired Electrical Engineer
winnie said:Charlie. . . On the use of 'average', do you consider "The American Heritage Dictionary" sufficiently authoritative?
I will accept that source as authoritative. Did you notice that,
winnie said:"A number that typifies a set of numbers of which it is a function."
Is not the same thing as
winnie said:. . . a function that is used to typify the magnitude of a constantly changing function.
In attempt to force-fit “RMS” into the definition of “average,” you altered the definition. Not allowed.
winnie said:Notice that meaning _b_ is "arithmetic mean", whereas meaning _a_ is the rather general.
Yes, “meaning a” is rather general. But the RMS value is not typical of the set of values of which it is a member. Most of the values in a sine wave are lower than the RMS value. The actual average, as you pointed out earlier, is zero. You will note that there are as many values higher than zero as there are lower than zero. On this basis, one can say that “zero” is a typical value. The concept of RMS does not fit the definition of “average.”
I have no interest in pursuing this further either. My one and only point here is that if you intend to teach, you have to be clear as to when you are being precise for the benefit of those students who come into the course with a basic understanding of the fundamental science, and when you are simplifying the concept for the sake of the students who do not.