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
- 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.
- 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
- The root mean square (RMS) is a statistical measure of the magnitude of a varying quantity.
- The root mean square (RMS) has an interesting relationship to the mean ($\bar{x}$) and the population standard deviation ($\sigma$), such that:
$$\mathrm{RMS}^2=\bar{x}^2+\sigma^2$$
Examples
Example 1:
|
|
Formula | Description (Result) |
---|---|
=RMS($B$2:$B$30) | Sample root mean square (1.282) |
Files Examples
Related Links
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
Comments
Article is closed for comments.