quadratic mean

mathematics

Also known as: root mean square

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July 13, 2026

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The quadratic mean, also known as the root mean square, is a mathematical concept used to find a value intermediate to a set of numbers. It is calculated by taking the square root of the arithmetic mean of the squares of those numbers.12

For a set of n numbers (x₁, x₂, ..., x_n), the quadratic mean (M₂) is expressed as:
[ M_2 = \sqrt{\frac{x_1^2 + x_2^2 + \dots + x_n^2}{n}} ]
This differs from the arithmetic mean, which is simply the sum of the numbers divided by n. The quadratic mean is particularly useful in statistics, as it relates to the standard deviation of a dataset.2

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mean
The number 4 is the quadratic mean (or root mean square) of the numbers 1, 1, 2, 5, and 7 and differs from their arithmetic mean, which is 3 1/5. In general, the quadratic mean of n numbers x₁, x₂, …, x_n is the square root of the…
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The number 4 is the quadratic mean (or root mean square) of the numbers 1, 1, 2, 5, and 7 and differs from their arithmetic mean, which is 3 1/5. In general, the quadratic mean of n numbers x₁, x₂, …, x_n is the square root of the…
Read More