Many people, including me, are most comfortable with arithmetic mean because it makes much sense to them. Think of three persons having 3, 7 and 5 apples. Behind every math concept there is a rational approach and logical reasoning.average

1 a : a single value (as a mean, mode, or median) that summarizes or represents the general significance of a set of unequal values

[M-W's Col. Dic.]

arithmetic mean = (3+7+5) / 3 = 15/3 = 5

It says that if apples are equally distributed then each person would receive 5 apples. It would make more sense when it is seen in a particular context in 'real' life.

This question about RMS value came to me when I read about Vrms. Yes, sinusoid is alternating between positive and negative values. In one half cycle it could be +1 and in next half cycle it would be -1. Saying that we have to take root mean square value (RMS) because it keeps alternating between +ve and -ve and gives us 'regular' average to be zero, (+1+(-1))/2 = 0, is little naive. Because one may argue that why not use absolute values of negative numbers such as (+1 + |-1|)/2 = +1.

There are many different kinds of mean. But we will focus on arithmetic mean and root mean square.

**1:**My first question is that in your opinion why there are so many different kinds of mean.

**2:**I understand that the problem under discussion would dictate which mean should be used. Under what circumstances RMS is used?

**3:**How would you differentiate between arithmetic mean and RMS? Their advantages and disadvantages. If we have values: 7 10 7 0 -3 -1 -2 0. It's RMS would be 5.14. I don't think it represents the 'average' of the values correctly. There is so much deviation.

Useful links:

http://en.wikipedia.org/wiki/Mean

http://www.bcae1.com/voltages.htm

http://en.wikipedia.org/wiki/Root_mean_square

http://www.rfcafe.com/references/electrical/square-wave-voltage-conversion.htm

http://cnx.org/content/m13418/latest/

http://www.practicalphysics.org/go/Guidance_107.html