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Built-in Mathematica SymbolSee Also »|More About »

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].
  • Standardize shifts by a location and rescales by a scale estimated from the elements of list.
  • Standardize[list, f1, f2] is effectively (list-f1[list])/f2[list].
  • Common choices for f1 and f2 include:
MeanStandardDeviationzero mean and unit variance
Mean1&shift to mean 0
Median1&shift by the median
0&StandardDeviationscale to have unit variance
  • Standardize[{{x1, y1, ...}, {x2, y2, ...}, ...}] effectively gives Transpose[{Standardize[{x1, x2, ...}], Standardize[{y1, y2, ...}], ...}].  »
EXAMPLESCLOSE ALL
Basic Examples   (3)
Compute standard scores for data:
Shift to have mean zero without scaling:
Shift by the Median and scale by the InterquartileRange:
Compute standard scores for data:
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Shift to have mean zero without scaling:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
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In[3]:=
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Out[3]=
 
Shift by the Median and scale by the InterquartileRange:
In[1]:=
Click for copyable input
Out[1]=
Scope   (4)
Standardize exact numeric data:
Symbolic values:
Standardize arbitrary-precision data:
Standardize matrix data by column:
Applications   (1)
Shift normally distributed values to a standard normal:
The theoretical curves:
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