The Root Mean Square, or quadratic mean, is a statistical function for finding the average of a series even if it contains negative numbers. When you have a series with negative numbers, the normal formula for averaging  adding all the numbers and dividing by the number of numbers  will give you the "middle value," but it won't give you a sense of the average magnitude. RMS tells you how big the average number is, no matter which side of the number line it's on. Most realworld RMS problems must use calculus, but you can find the RMS of a small series with basic math and a calculator.
Things You'll Need
 Calculator

Count the number of numerals you are finding the RMS for. For example, if you have the series 5, 3 and 7, you have three numerals.

Square each of the numbers, either in your head or with a calculator. Write each one down on a piece of paper as you go so you don't lose track of them. For example, the squares of 5, 3 and 7 are 25, 9 and 49.

Add all the squares together. For our series, 25 + 9 + 49 = 83.

Divide the sum of the squares by the number of numbers. 83 divided by 3 is 27.67.

Take the square root of the sum divided by the number of numbers. The square root of 27.67 is 5.26, so for the series 5, 3 and 7, the RMS is 5.26.
References
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