The Root Mean Square (R.M.S.) is a measure used to determine the average magnitude of a set of numbers, especially when dealing with values that can be both positive and negative. It is often used in physics, engineering, and statistics to compute energy, voltage, and deviations.
\[ \text{R.M.S.} = \sqrt{\frac{1}{n} \sum x_i^2} \]
Where:
\[ \text{R.M.S.} \geq \bar{x} \ (\text{A.M.}) \geq \text{G.M.} \geq \text{H.M.} \]
This inequality shows that for any set of positive numbers, Root Mean Square is always greater than or equal to Arithmetic Mean (A.M.), which is greater than or equal to Geometric Mean (G.M.), and so on.