WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home Page »

RootMeanSquare
✖
RootMeanSquare

✖

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

open allclose all

Basic Examples  (3)Summary of the most common use cases

RootMeanSquare of a list:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-xif
Out[1]=1

RootMeanSquare of columns of a matrix:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-vu6sr
Out[1]=1

RootMeanSquare of a parametric distribution:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-n3bzeg
Out[1]=1

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

Data  (10)

Exact input yields exact output:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-ug7y2
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-bcry2t
Out[2]=2

Approximate input yields approximate output:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-ksx55
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-d02ofx
Out[2]=2

RootMeanSquare for a matrix gives columnwise means:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-ezu2uz
Out[1]=1

Works with large arrays:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-nknun
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-ma3v2m
Out[2]=2

SparseArray data can be used just like dense arrays:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-n691tv
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-drrysl
Out[2]=2

Compute results for a SparseArray:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-l4ct3
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-d6csj0
Out[2]=2

RootMeanSquare for WeightedData:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-d0wc9z
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-f1vfw
In[3]:=3
✖
https://wolfram.com/xid/0g7itfcdyf2-qyv0h
Out[3]=3

RootMeanSquare for EventData:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-e67u14
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-or2nrz
Out[2]=2

RootMeanSquare for TimeSeries:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-hf056t
Out[1]=1

The root mean square depends only on the values:

In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-ikztk4
Out[2]=2

RootMeanSquare for data involving quantities:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-jopin9
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-e8c21s
Out[2]=2

Distributions and Processes  (4)

Find the RootMeanSquare for univariate distributions:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-rxz55
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-hbq28j
Out[2]=2

Multivariate distributions:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-ek075b
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-lzwoz3
Out[2]=2

RootMeanSquare for derived distributions:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-rgc72x
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-byqvvz
Out[2]=2

Data distribution:

In[3]:=3
✖
https://wolfram.com/xid/0g7itfcdyf2-215ry
In[4]:=4
✖
https://wolfram.com/xid/0g7itfcdyf2-fq5ptk
Out[4]=4

RootMeanSquare for distributions with quantities:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-dqsioj
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-b53jwg
Out[2]=2

RootMeanSquare for a random process:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-fugn
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-g9pmgp
Out[2]=2

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

Root mean square error for a linear fit:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-lqzjie
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-p1u03
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0g7itfcdyf2-cab9e7
Out[3]=3

Sample a periodic signal:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-cwptf9
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-dkujrt
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0g7itfcdyf2-yv2c2
Out[3]=3

Compute the root mean square value of the sample:

In[4]:=4
✖
https://wolfram.com/xid/0g7itfcdyf2-csnxk
Out[4]=4

Compare with the exact value:

In[5]:=5
✖
https://wolfram.com/xid/0g7itfcdyf2-ekvqot
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0g7itfcdyf2-c3rp5t
Out[6]=6

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

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-cevfij
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-fllmtw
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0g7itfcdyf2-celepo
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0g7itfcdyf2-cny2bx
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:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-793v1
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-b9x4up
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0g7itfcdyf2-bhsxlb
Out[3]=3

RootMeanSquare is equivalent to a scaled Norm:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-jxw4y8
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-drqfrx
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0g7itfcdyf2-cuwc0b
Out[3]=3

RootMeanSquare of deviations is equivalent to a scaled StandardDeviation:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-m0xfm
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-hh6mz4
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0g7itfcdyf2-i5cfjy
Out[3]=3

RootMeanSquare of deviations is the square root of a CentralMoment:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-dso2q7
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-vy95m
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0g7itfcdyf2-hfsstq
Out[3]=3

RootMeanSquare is a scaled EuclideanDistance from the Mean:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-hx9oab
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-cg5jg0
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0g7itfcdyf2-pf9xkh
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0g7itfcdyf2-zp24k
Out[4]=4

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

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-c5emif
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-cl5rpb
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0g7itfcdyf2-ekl2fe
Out[3]=3

RootMeanSquare is a measure of scale:

In[1]:=1
✖
https://wolfram.com/xid/0g7itfcdyf2-bhnrki
In[2]:=2
✖
https://wolfram.com/xid/0g7itfcdyf2-t94no
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0g7itfcdyf2-o9323q
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_2025_rootmeansquare, author="Wolfram Research", title="{RootMeanSquare}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/RootMeanSquare.html}", note=[Accessed: 06-April-2025 ]}

✖
@misc{reference.wolfram_2025_rootmeansquare, author="Wolfram Research", title="{RootMeanSquare}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/RootMeanSquare.html}", note=[Accessed: 06-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_rootmeansquare, organization={Wolfram Research}, title={RootMeanSquare}, year={2017}, url={https://reference.wolfram.com/language/ref/RootMeanSquare.html}, note=[Accessed: 06-April-2025 ]}

✖
@online{reference.wolfram_2025_rootmeansquare, organization={Wolfram Research}, title={RootMeanSquare}, year={2017}, url={https://reference.wolfram.com/language/ref/RootMeanSquare.html}, note=[Accessed: 06-April-2025 ]}