different kinds of mean, arithmetic mean, root mean square (RMS) etc.

[PG1995]

Hi

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.]

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.

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/
**broken link removed**

 

[squishy36]

The short answer is that these different "measures of central tendency" (that's what statisticians call them) have various uses. The usual arithmetic mean is probably meaningful to you because you're most familiar with it -- and it's the most commonly used statistically when making measurements. But sometimes in experimentation you'll find uses for other measures such as the median, mode, or geometric mean. The first two can pop up when you're doing nonparametric statistics.

RMS is used in electronics because of a very important experimental fact: it predicts the Joule heating of an electrical current. Note the arithmetical average doesn't do that, which makes it useless for such predictions. Tip: you might want to investigate the similarities between RMS and the statistical sample standard deviation. The standard deviation is a measure of the "dispersion" of the sample's values from the mean value. That should ring a physical intuition bell for electrical measurements of AC stuff.

 

[Ratchit]

PG1995,

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

Because they exist. The same as asking; "Why are there so many number values?"

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

When determining the relative energy of a wave of varying values to an equivalent DC energy value.

How would you differentiate between arithmetic mean and RMS?

By the way they are calculated.

Their advantages and disadvantages.

Dumb question. Like asking what is more advantageous, voltage or current.

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.

Correct, and rightly so, especially when we want the RMS, and not the mean, median, mode, harmonic, or geometric average.

There is so much deviation.

It is deliberate deviation.

Ratch

 

[MrAl]

Hi



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.

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/
**broken link removed**

Hi there,

As others have already alluded to, there are many different kinds of mean calculation types simply because there are many different kinds of applications, where the various applications can benefit better using one type of mean calculation than another. It's as simple as that.

These kinds of calculations arise in real life, and people come up with formulas to deal with them or borrow formulas from other areas that happen to work there too.

An example exercise would be to try to come up with a formula on your own that prints out a table of standard five percent (5%) tolerance resistors. Here, we want to print out specific values like 3.9k, 4.7k, but we dont want garbage like 3.912489k or 4.69999k. We want the actual value that we would go out and purchase.

One way to approach this is to use curve fitting, where we would use what is known as the "Least Squares" curve fitting criterion. This simply means we will come up with a trial formula using our imagination and try to fit the known standard values to the curve, where the errors are squared and summed (similar to the mean although we dont necessarily have to divide anything).
We might however find that we can get a better fit using the "Sum of Absolute Maximums" which is also like a mean without having to divide (we could divide if we wanted to however in both cases).

So you see how simple it really is, we choose whichever fits the application better. Usually it's because it represents some key point of the problem better.

If you went out to buy oranges you might see a sign that says "3 for 2 dollars", but if you went out to buy grapes you might see a sign that says "$1.49 a pound".
Why a given quantity in one case and a given weight in another case?
The way the final cost is calculated is simplest in each case, so that technique is used.

Unless of course you prefer to count all your grapes, one by one