RMS vs Average
To understand the difference between RMS and Average, it is necessary to know what is average (or mean) and what is RMS (Root Mean Square). RMS and Average are two mathematical concepts used to describe the overall nature of a collection of numbers. The usage is extended into the physical sciences and related technologies in the same context. Average is rather a familiar and intuitive concept while RMS is a concept explicitly based on a mathematical definition. Let’s look at their definitions and the methods of calculating average and RMS values in detail.
What is Mean (or Average) Value?
In mathematics, mean is a summarizing of a series of values to give a general impression of the collection. It is also used as a descriptive statistic, hence considered a measure of central tendency.
The mean is calculated in different ways, based on the application. Therefore, the exact mathematical definition of mean varies: those are the arithmetic mean, geometric mean, harmonic mean, and weighted mean. Their definitions are as follows.
Where xi represent the data values and wi are the weight of each value. It is worth noting that AM, GM, and HM satisfy the following uncertainty, AM≥GM≥HM.
Weighted mean can be considered as an extension of the arithmetic mean. Truncated mean, Interquartile mean, and Winsorized mean are also used in specific cases, but the first three types of mean known as the Pythagorean Means are the most commonly used means.
What is RMS – Root Mean Square Value?
In some applications, the simple Pythagorean means are no proper indication of the sample data. For example, consider a time varying sinusoidal electronic signal with no voltage shift. The average of the amplitude within a cycle is zero implying that the voltage within that period was zero, which physically is untrue. As a result, any calculations involving the values are incorrect.
For example, the energy calculated gives incorrect values. If the maximum or minimum values of the signal are considered, still the answers are a distant form reasonable indication. Analyzing the root cause it is evident that the fluctuations from negative to positive cause the values to cancel each other out when they are summed up together. Therefore, the values must be added in a way that they do not cancel each other.
Squared mean or the RMS values can be considered as an alternative. Root mean square value is defined as,
The voltage and current in the power mains, in our households, are indicating the RMS values of the voltages and current of the alternating source voltage. The idea of the squared mean can be extended to a more general case (all the symbols have the usual meaning):
What is the difference between RMS and Average (Mean)?
- The mean is a summarization of a collection of numbers which is a measure of central tendency for a sample of the population, and it is an important descriptive statistic.
- The mean is defined mathematically in different ways, and the interpretation is most valid based on the application.
- Arithmetic Mean is the sum of all the considered data values divided by the number of data values, which gives a single number to represent the whole data set. When there are both negative and positive numbers, they cancel out and based on the scenario that value might not represent the data set in a valid manner.
- In arithmetic mean, the sum of the data values is taken without any changes made to that.
- In RMS, the data values are squared, and after taking the arithmetic mean of those squared values, square root of that number is taken.