# Difference Between RMS and Average

**RMS vs Average**

Average

The term average is from mathematics that basically means the central tendency of a set particular set of data. There are actually a lot of ways to describe an average. An average can be the (arithmetic) mean, mode, or median.

Having said that, the most commonly associated with the term average is the ‘arithmetic mean’. It is the sum of all values given in data set and divided by total number of values.

Mathematically, the average, as an arithmetic mean, is written this way:

Average = (X + X2 + X3 + X4 + X5 + ‘¦’¦.) / n

Where:

X, X2, X3, X4, X5, and so on = any value

n = number of values given

Average is often used in all fields of engineering and mathematics, especially in statistics. It is in fact a part of more complex way of solving things like the RMS which will be taken up next.

RMS

RMS means ‘Root Mean Square’ in mathematics. It is also referred to as quadratic mean. The RMS is very useful in many fields, particularly in electrical engineering and in the domain of signal amplifiers. RMS is very useful when the random variables in the data are negative and positive such as sinusoids.

In descriptive mathematics, it is the square root of the average or arithmetic mean of all the squares of values or usually the square of the function that describes a continuous waveform. In electrical engineering, it would mean the instantaneous values of current or voltage in an AC circuit and in this field, RMS is a technique that is extensively used. It is also known as the effective value.

Mathematically,

RMS = âˆš[(X2 + X22 + X32 + X42 + X52 + ‘¦.) / n]

Where:

X, X2, X3, X4, X5, and so on = any value

n = number of values given

Summary:

1.RMS is more mathematically complex that involves averages.

2.Average can be expressed in many ways (e.g. mean, median, or mode). In RMS, the average, expressed as an arithmetic mean is used.

3.Average is used to get the central tendency of a given data set while RMS is used when random variables given in the data are negative and positive such as sinusoids.

4.Average is broadly used in any scientific and engineering field you can think of while RMS is rather specific in its practical usage.

5.Average is a staple in statistics while RMS is significantly relevant in electrical engineering and signal sciences.

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As you said, RMS is preferred where positive and negative both values are present.

My concern is then why we don’t use always RMS values, and dump the concept average value.

Or is there some application where Mean should be preferable over RMS.

Pls reply