# RootMeanSquare

RootMeanSquare[list]

gives the root mean square of values in list.

RootMeanSquare[dist]

gives the root mean square of the distribution dist.

# Details • RootMeanSquare measures scale of data or distributions.
• RootMeanSquare[list] gives the square root of the second sample moment.
• For the list {x1,x2,,xn}, the root mean square is given by .
• RootMeanSquare handles both numerical and symbolic data.
• RootMeanSquare[{{x1,y1,},{x2,y2,},}] gives {RootMeanSquare[{x1,x2,}],RootMeanSquare[{y1,y2,}]}.
• RootMeanSquare[dist] is equivalent to Sqrt[Expectation[x2,xdist]].

# Examples

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## Basic Examples(3)

RootMeanSquare of a list:

RootMeanSquare of columns of a matrix:

RootMeanSquare of a parametric distribution:

## Scope(14)

### Data(10)

Exact input yields exact output:

Approximate input yields approximate output:

RootMeanSquare for a matrix gives column-wise means:

Works with large arrays:

SparseArray data can be used just like dense arrays:

Compute results for a SparseArray:

The root mean square depends only on the values:

RootMeanSquare for data involving quantities:

### Distributions and Processes(4)

Find the RootMeanSquare for univariate distributions:

Multivariate distributions:

RootMeanSquare for derived distributions:

Data distribution:

RootMeanSquare for distributions with quantities:

RootMeanSquare for a random process:

## Applications(3)

Root mean square error for a linear fit:

Sample a periodic signal:

Compute the root mean square value of the sample:

Compare with the exact value:

Find the root mean square value for the heights of children in a class:

## Properties & Relations(7)

RootMeanSquare is the square root of the Mean of the data squared:

RootMeanSquare is equivalent to a scaled Norm:

RootMeanSquare of deviations is equivalent to a scaled StandardDeviation:

RootMeanSquare of deviations is the square root of a CentralMoment:

RootMeanSquare is a scaled EuclideanDistance from the Mean:

RootMeanSquare of a random variable is the square root of an Expectation:

RootMeanSquare is a measure of scale: