WOLFRAM

gives the root mean square of values in list.

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)Summary of the most common use cases

RootMeanSquare of a list:

Out[1]=1

RootMeanSquare of columns of a matrix:

Out[1]=1

RootMeanSquare of a parametric distribution:

Out[1]=1

Scope  (14)Survey of the scope of standard use cases

Data  (10)

Exact input yields exact output:

Out[1]=1
Out[2]=2

Approximate input yields approximate output:

Out[1]=1
Out[2]=2

RootMeanSquare for a matrix gives columnwise means:

Out[1]=1

Works with large arrays:

Out[1]=1
Out[2]=2

SparseArray data can be used just like dense arrays:

Out[1]=1
Out[2]=2

Compute results for a SparseArray:

Out[1]=1
Out[2]=2

RootMeanSquare for WeightedData:

Out[1]=1
Out[3]=3

RootMeanSquare for EventData:

Out[2]=2

RootMeanSquare for TimeSeries:

Out[1]=1

The root mean square depends only on the values:

Out[2]=2

RootMeanSquare for data involving quantities:

Out[1]=1
Out[2]=2

Distributions and Processes  (4)

Find the RootMeanSquare for univariate distributions:

Out[1]=1
Out[2]=2

Multivariate distributions:

Out[1]=1
Out[2]=2

RootMeanSquare for derived distributions:

Out[1]=1
Out[2]=2

Data distribution:

Out[4]=4

RootMeanSquare for distributions with quantities:

Out[1]=1
Out[2]=2

RootMeanSquare for a random process:

Out[1]=1
Out[2]=2

Applications  (3)Sample problems that can be solved with this function

Root mean square error for a linear fit:

Out[2]=2
Out[3]=3

Sample a periodic signal:

Out[2]=2
Out[3]=3

Compute the root mean square value of the sample:

Out[4]=4

Compare with the exact value:

Out[5]=5
Out[6]=6

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

Out[2]=2
Out[3]=3
Out[4]=4

Properties & Relations  (7)Properties of the function, and connections to other functions

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

Out[2]=2
Out[3]=3

RootMeanSquare is equivalent to a scaled Norm:

Out[2]=2
Out[3]=3

RootMeanSquare of deviations is equivalent to a scaled StandardDeviation:

Out[2]=2
Out[3]=3

RootMeanSquare of deviations is the square root of a CentralMoment:

Out[2]=2
Out[3]=3

RootMeanSquare is a scaled EuclideanDistance from the Mean:

Out[2]=2
Out[3]=3
Out[4]=4

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

Out[2]=2
Out[3]=3

RootMeanSquare is a measure of scale:

Out[2]=2
Out[3]=3
Wolfram Research (2007), RootMeanSquare, Wolfram Language function, https://reference.wolfram.com/language/ref/RootMeanSquare.html (updated 2017).
Wolfram Research (2007), RootMeanSquare, Wolfram Language function, https://reference.wolfram.com/language/ref/RootMeanSquare.html (updated 2017).

Text

Wolfram Research (2007), RootMeanSquare, Wolfram Language function, https://reference.wolfram.com/language/ref/RootMeanSquare.html (updated 2017).

Wolfram Research (2007), RootMeanSquare, Wolfram Language function, https://reference.wolfram.com/language/ref/RootMeanSquare.html (updated 2017).

CMS

Wolfram Language. 2007. "RootMeanSquare." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/RootMeanSquare.html.

Wolfram Language. 2007. "RootMeanSquare." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/RootMeanSquare.html.

APA

Wolfram Language. (2007). RootMeanSquare. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RootMeanSquare.html

Wolfram Language. (2007). RootMeanSquare. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RootMeanSquare.html

BibTeX

@misc{reference.wolfram_2024_rootmeansquare, author="Wolfram Research", title="{RootMeanSquare}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/RootMeanSquare.html}", note=[Accessed: 20-December-2024 ]}

@misc{reference.wolfram_2024_rootmeansquare, author="Wolfram Research", title="{RootMeanSquare}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/RootMeanSquare.html}", note=[Accessed: 20-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_rootmeansquare, organization={Wolfram Research}, title={RootMeanSquare}, year={2017}, url={https://reference.wolfram.com/language/ref/RootMeanSquare.html}, note=[Accessed: 20-December-2024 ]}

@online{reference.wolfram_2024_rootmeansquare, organization={Wolfram Research}, title={RootMeanSquare}, year={2017}, url={https://reference.wolfram.com/language/ref/RootMeanSquare.html}, note=[Accessed: 20-December-2024 ]}