# 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:
$$\mathrm{RMS}^2=\bar{x}^2+\sigma^2$$

## Examples

Example 1:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
A B
Date Data
1/1/2008 #N/A
1/2/2008 -1.28
1/3/2008 0.24
1/4/2008 1.28
1/5/2008 1.20
1/6/2008 1.73
1/7/2008 -2.18
1/8/2008 -0.23
1/9/2008 1.10
1/10/2008 -1.09
1/11/2008 -0.69
1/12/2008 -1.69
1/13/2008 -1.85
1/14/2008 -0.98
1/15/2008 -0.77
1/16/2008 -0.30
1/17/2008 -1.28
1/18/2008 0.24
1/19/2008 1.28
1/20/2008 1.20
1/21/2008 1.73
1/22/2008 -2.18
1/23/2008 -0.23
1/24/2008 1.10
1/25/2008 -1.09
1/26/2008 -0.69
1/27/2008 -1.69
1/28/2008 -1.85
1/29/2008 -0.98

Formula Description (Result)
=RMS($B$2:$B$30) Sample root mean square (1.282)