WOLFRAM

Wolfram Language & System Documentation Center

Standardize[list]

shifts and rescales the elements of list to have zero mean and unit sample variance.

Standardize[list,f1]

shifts the elements in list by f1[list] and rescales them to have unit sample variance.

Standardize[list,f1,f2]

shifts by f1[list] and scales by f2[list].

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

Standardize

Standardize[list]

shifts and rescales the elements of list to have zero mean and unit sample variance.

Standardize[list,f1]

shifts the elements in list by f1[list] and rescales them to have unit sample variance.

Standardize[list,f1,f2]

shifts by f1[list] and scales by f2[list].

Details

Examples

open all close all

Basic Examples  (3)

Compute standard scores for data:

Wolfram Language code: Standardize[{6.5, 3.8, 6.6, 5.7, 6.0, 6.4, 5.3}]
Wolfram Language code: {Mean[%], Variance[%]}

Shift to have mean zero without scaling:

Wolfram Language code: Standardize[{6.5, 3.8, 6.6, 5.7, 6.0, 6.4, 5.3}, Mean, 1&]
Wolfram Language code: {Mean[%], Variance[%]}

Shift to Median with standard scaling:

Wolfram Language code: Standardize[{6.5, 3.8, 6.6, 5.7, 6.0, 6.4, 5.3}, Median]
Wolfram Language code: {Mean[%], Median[%], Variance[%]}

Shift to Median and scale by the InterquartileRange:

Wolfram Language code: Standardize[{6.5, 3.8, 6.6, 5.7, 6.0, 6.4, 5.3}, Median, InterquartileRange]
Wolfram Language code: {Mean[%], Median[%], Variance[%], InterquartileRange[%]}

Scope  (6)

Standardize exact numeric data:

Wolfram Language code: Standardize[Range[5]]

Symbolic values:

Wolfram Language code: Simplify[Standardize[{a, b, c}], {a, b, c}∈Reals]

Standardize arbitrary‐precision data:

Wolfram Language code: Standardize[N[Range[5], 20]]

Standardize matrix data by column:

Wolfram Language code: data = RandomReal[10, {10, 3}]
Wolfram Language code: Standardize[data]
Wolfram Language code: {Mean[%], Variance[%]}//Chop

Standardize a TimeSeries:

Wolfram Language code: ts = TemporalData[TimeSeries, {{{-0.8665776485273015, -0.6782110300443249, -0.5060797754514599, -1.544046353019984, -1.548861927442106, 2.268550811187895, 0.7674881482532252, -0.33377919918496324, -0.2623443622275032, -0.7898169819548497, -0.2 ... 5074135634818395, -7.993517405936538, -8.11824028466883, -7.421451285939192, -7.617297878523265, -8.63887295423076}}, {{0, 78, 1}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> None}}, False, 10.1];
Wolfram Language code: {Mean[ts], Variance[ts]}
Wolfram Language code: res = Standardize[ts]
Wolfram Language code: {Mean[res], Variance[res]}//Chop

Standardize a SparseArray:

Wolfram Language code: sp = SparseArray[RandomInteger[1, 10]]
Wolfram Language code: Standardize[sp]

Applications  (3)

Shift normally distributed values to a standard normal:

Wolfram Language code: data = RandomReal[NormalDistribution[5, 2], 500];
Wolfram Language code: sdata = Standardize[data];
Wolfram Language code: {ListPlot[Sort[data]], ListPlot[Sort[sdata]]}

The theoretical curves:

Wolfram Language code: {Plot[InverseCDF[NormalDistribution[Mean[data], StandardDeviation[data]], q], {q, 0, 1}], Plot[InverseCDF[NormalDistribution[], q], {q, 0, 1}]}

Center a data matrix by subtracting column means:

Wolfram Language code: data = RandomReal[10, {5, 3}]
Wolfram Language code: cdata = Standardize[data, Mean, 1&]

The mean of the centered data is 0:

Wolfram Language code: Mean[cdata]//Chop

The covariance structure is unchanged:

Wolfram Language code: MatrixForm /@ {Covariance[data], Covariance[cdata]}

Use Standardize to centralize a TimeSeries:

Wolfram Language code: ts = TemporalData[TimeSeries, {{{-0.8665776485273015, -0.6782110300443249, -0.5060797754514599, -1.544046353019984, -1.548861927442106, 2.268550811187895, 0.7674881482532252, -0.33377919918496324, -0.2623443622275032, -0.7898169819548497, -0.2 ... 5074135634818395, -7.993517405936538, -8.11824028466883, -7.421451285939192, -7.617297878523265, -8.63887295423076}}, {{0, 78, 1}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> None}}, False, 10.1];
Wolfram Language code: Mean[ts]

Centralize:

Wolfram Language code: res = Standardize[ts, Mean, 1&]
Wolfram Language code: Mean[res]//Chop

The variance is unchanged:

Wolfram Language code: Variance[ts] == Variance[res]

Properties & Relations  (1)

Compute MeanDeviation using Standardize:

Wolfram Language code: data = RandomReal[10, 20]
Wolfram Language code: Mean[Abs[Standardize[data, Mean, 1&]]]
Wolfram Language code: MeanDeviation[data]

Similarly compute MedianDeviation:

Wolfram Language code: Median[Abs[Standardize[data, Median, 1&]]]
Wolfram Language code: MedianDeviation[data]
Wolfram Research (2008), Standardize, Wolfram Language function, https://reference.wolfram.com/language/ref/Standardize.html.

Text

Wolfram Research (2008), Standardize, Wolfram Language function, https://reference.wolfram.com/language/ref/Standardize.html.

CMS

Wolfram Language. 2008. "Standardize." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Standardize.html.

APA

Wolfram Language. (2008). Standardize. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Standardize.html

BibTeX

@misc{reference.wolfram_2026_standardize, author="Wolfram Research", title="{Standardize}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Standardize.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_standardize, organization={Wolfram Research}, title={Standardize}, year={2008}, url={https://reference.wolfram.com/language/ref/Standardize.html}, note=[Accessed: 13-June-2026]}