Understanding RMS vs. Absolute Value for Calculating Averages in Data Analysis

[gsingh2011]

I never really understood why using the Root Mean Square of negative data is the preferred method of finding the average of the data as opposed to taking the absolute value of the data and taking the average (arithmetic mean) of that. The example that recently made me wonder about this is alternating current. The RMS current is the maximum current divided by root two. But why isn't the average current simply the average value after taking the absolute value of the current?

 

[ych22]

I never really understood why using the Root Mean Square of negative data is the preferred method of finding the average of the data as opposed to taking the absolute value of the data and taking the average (arithmetic mean) of that. The example that recently made me wonder about this is alternating current. The RMS current is the maximum current divided by root two. But why isn't the average current simply the average value after taking the absolute value of the current?

THe RMS current is not the average current, it is the root of the average squared current. You do not use RMS current/average current interchangeably, I believe (but hey I'm not a physicist/EE)

 

[bpet]

The RMS current is useful because it's directly related to the power consumption.

 

[vk6kro]

I never really understood why using the Root Mean Square of negative data is the preferred method of finding the average of the data as opposed to taking the absolute value of the data and taking the average (arithmetic mean) of that. The example that recently made me wonder about this is alternating current. The RMS current is the maximum current divided by root two. But why isn't the average current simply the average value after taking the absolute value of the current?

The difference is that power depends on the square of the voltage, not just the voltage.
The RMS voltage of a waveform is the DC voltage that would have the same heating effect as the this waveform.

So, the parts of the waveform that are twice as big as others have 4 times as much heating ability.

The average voltage of a sinewave (allowing for absolute values) is 0.637 times the peak value, but the RMS value is 0.707 times the peak value.
The difference between these values is due to the heating effect of the parts of the sinewave near the peak value.

 

[blue_raver22]

I understand your confusion about using RMS (Root Mean Square) versus absolute value for calculating averages in data analysis. Allow me to provide some clarification on this topic.

First, it is important to note that the choice of using RMS or absolute value for calculating averages depends on the type of data and the purpose of the analysis. In some cases, using absolute value may be more appropriate, while in others, RMS is the preferred method.

In the case of alternating current, the RMS value is used because it takes into account the alternating nature of the current. This is important because the average value of an alternating current over a period of time is not representative of the actual amplitude of the current. By using RMS, we are able to calculate the average power of the current, which is a more accurate representation of the overall energy being transferred.

On the other hand, taking the absolute value and calculating the average would not accurately reflect the energy being transferred in an alternating current. This is because the absolute value would only consider the magnitude of the current, without taking into account the direction of the current flow.

In addition, RMS is a more mathematically sound method for calculating averages. The arithmetic mean of absolute values can be biased by extreme values, leading to an inaccurate representation of the data. RMS, on the other hand, is not affected by extreme values and provides a more stable measure of the average.

In conclusion, while it may seem counterintuitive to use RMS instead of absolute value for calculating averages, it is a more accurate and reliable method for certain types of data, such as alternating current. As scientists, it is important to carefully consider the type of data and the purpose of our analysis in order to choose the most appropriate method for calculating averages.