RMS - Root Mean Square

Returns the sample root mean square (RMS).

Syntax

RMS(X)

X

is the input data sample (one/two-dimensional array of cells (e.g., rows or columns)).

Remarks

1. The input time series data may include missing values (e.g., #N/A, #VALUE!, #NUM!, empty cell), but they will not be included in the calculations.
2. The root mean square (RMS) is defined as follows for a set of $n$ values ${x_1,x_2,...,x_n}$: $$\mathrm{RMS}=\sqrt{\frac{x_1^2+x_2^2+\cdots +x_N^2}{N}} =\sqrt{\frac{\sum_{i=1}^N {x_i^2}}{N}}$$ Where:
   • $x_i$ is the value of the i-th non-missing observation,
   • $N$ is the number of non-missing observations in the input sample data,
3. The root mean square (RMS) is a statistical measure of the magnitude of a varying quantity.
4. The root mean square (RMS) has an interesting relationship to the mean ($\bar{x}$) and the population standard deviation ($\sigma$), such that: $$\mathrm{RMS}^2=\bar{x}^2+\sigma^2$$

Files Examples

Related Links

• Wikipedia - Root mean square.

References

• Hamilton, J .D.; Time Series Analysis, Princeton University Press (1994), ISBN 0-691-04289-6.
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740.