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Standardize
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Standardize

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Standardize[list]

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

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Standardize[list,f1]

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

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Standardize[list,f1,f2]

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

Details

Examples

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

Compute standard scores for data:

In[1]:=1
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https://wolfram.com/xid/09a7l22hq-c635x8
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09a7l22hq-fq919n
Out[2]=2

Shift to have mean zero without scaling:

In[1]:=1
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https://wolfram.com/xid/09a7l22hq-cleo4q
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09a7l22hq-dw2pfd
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/09a7l22hq-srglo
Out[3]=3

Shift by the Median and scale by the InterquartileRange:

In[1]:=1
✖
https://wolfram.com/xid/09a7l22hq-dhwfit
Out[1]=1

Scope  (5)Survey of the scope of standard use cases

Standardize exact numeric data:

In[1]:=1
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https://wolfram.com/xid/09a7l22hq-fy2q9z
Out[1]=1

Symbolic values:

In[1]:=1
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https://wolfram.com/xid/09a7l22hq-h4hpx
Out[1]=1

Standardize arbitrary‐precision data:

In[1]:=1
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https://wolfram.com/xid/09a7l22hq-bhvmrb
Out[1]=1

Standardize matrix data by column:

In[1]:=1
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https://wolfram.com/xid/09a7l22hq-f0108z
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09a7l22hq-28ret
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/09a7l22hq-h8vgv
Out[3]=3

Standardize a TimeSeries:

In[1]:=1
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https://wolfram.com/xid/09a7l22hq-hqe0i1
In[2]:=2
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https://wolfram.com/xid/09a7l22hq-lnnu41
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/09a7l22hq-cnj275
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/09a7l22hq-v2egnq
Out[4]=4

Generalizations & Extensions  (1)Generalized and extended use cases

Standardize a SparseArray:

In[1]:=1
✖
https://wolfram.com/xid/09a7l22hq-bczqaw
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09a7l22hq-dgo8p9
Out[2]=2

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

Shift normally distributed values to a standard normal:

In[1]:=1
✖
https://wolfram.com/xid/09a7l22hq-kgi8pj
In[2]:=2
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https://wolfram.com/xid/09a7l22hq-oai6vw
In[3]:=3
✖
https://wolfram.com/xid/09a7l22hq-o9fsj8
Out[3]=3

The theoretical curves:

In[4]:=4
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https://wolfram.com/xid/09a7l22hq-lawgvq
Out[4]=4

Center a data matrix by subtracting column means:

In[1]:=1
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https://wolfram.com/xid/09a7l22hq-firuc1
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09a7l22hq-efgbgv
Out[2]=2

The mean of the centered data is 0:

In[3]:=3
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https://wolfram.com/xid/09a7l22hq-jni4sg
Out[3]=3

The covariance structure is unchanged:

In[4]:=4
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https://wolfram.com/xid/09a7l22hq-brbckh
Out[4]=4

Use Standardize to centralize a TimeSeries:

In[1]:=1
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https://wolfram.com/xid/09a7l22hq-w3egqr
In[2]:=2
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https://wolfram.com/xid/09a7l22hq-25463m
Out[2]=2

Centralize:

In[3]:=3
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https://wolfram.com/xid/09a7l22hq-9fd2o6
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/09a7l22hq-3t3v2a
Out[4]=4

The variance is unchanged:

In[5]:=5
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https://wolfram.com/xid/09a7l22hq-sngw9f
Out[5]=5

Properties & Relations  (1)Properties of the function, and connections to other functions

Compute MeanDeviation using Standardize:

In[1]:=1
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https://wolfram.com/xid/09a7l22hq-k4ybqn
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09a7l22hq-heeb5k
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/09a7l22hq-hkl9md
Out[3]=3

MedianDeviation:

In[4]:=4
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https://wolfram.com/xid/09a7l22hq-fuwtup
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/09a7l22hq-wd9
Out[5]=5
Wolfram Research (2008), Standardize, Wolfram Language function, https://reference.wolfram.com/language/ref/Standardize.html.
✖
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.

✖
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.

✖
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

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

BibTeX

@misc{reference.wolfram_2025_standardize, author="Wolfram Research", title="{Standardize}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Standardize.html}", note=[Accessed: 22-April-2025 ]}

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@misc{reference.wolfram_2025_standardize, author="Wolfram Research", title="{Standardize}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Standardize.html}", note=[Accessed: 22-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_standardize, organization={Wolfram Research}, title={Standardize}, year={2008}, url={https://reference.wolfram.com/language/ref/Standardize.html}, note=[Accessed: 22-April-2025 ]}

✖
@online{reference.wolfram_2025_standardize, organization={Wolfram Research}, title={Standardize}, year={2008}, url={https://reference.wolfram.com/language/ref/Standardize.html}, note=[Accessed: 22-April-2025 ]}