Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
Mathematica > Data Manipulation > Statistics > Descriptive Statistics >
Mathematica > Mathematics and Algorithms > Statistics > Descriptive Statistics >
Built-in Mathematica SymbolTutorials »|See Also »|More About »

Quantile

Quantile[list, q]
gives the q^(th) quantile of list.
Quantile[list, {q1, q2, ...}]
gives a list of quantiles q1, q2, ... .
Quantile[list, q, {{a, b}, {c, d}}]
uses the quantile definition specified by parameters a, b, c, d.
Quantile[dist, q]
gives a quantile of the symbolic distribution dist.
  • Quantile[{{x1, y1, ...}, {x2, y2, ...}, ...}, q] gives {Quantile[{x1, x2, ...}, q], Quantile[{y1, y2, ...}, q]}.
  • For a list of length n, Quantile[list, q, {{a, b}, {c, d}}] depends on x=a+(n+b)q. If x is an integer, the result is s[[x]], where s=Sort[list, Less]. Otherwise the result is s[[Floor[x]]]+(s[[Ceiling[x]]]-s[[Floor[x]]])(c+dFractionalPart[x]), with the indices taken to be 1 or n if they are out of range.
  • The default choice of parameters is {{0, 0}, {1, 0}}.
  • Common choices of parameters include:
{{0, 0}, {1, 0}}inverse empirical CDF (default)
{{0, 0}, {0, 1}}linear interpolation (California method)
{{1/2, 0}, {0, 0}}element numbered closest to qn
{{1/2, 0}, {0, 1}}linear interpolation (hydrologist method)
{{0, 1}, {0, 1}}mean-based estimate (Weibull method)
{{1, -1}, {0, 1}}mode-based estimate
{{1/3, 1/3}, {0, 1}}median-based estimate
{{3/8, 1/4}, {0, 1}}normal distribution estimate
  • Quantile[list, q] always gives a result equal to an element of list.
  • The same is true whenever d=0.
  • When d=1, Quantile is piecewise linear as a function of q.
  • Median[list] is equivalent to Quantile[list, 1/2, {{1/2, 0}, {0, 1}}].
  • About ten different choices of parameters are in use in statistical work.
EXAMPLESCLOSE ALL
Basic Examples   (4)
Find the half-way value (median) of a list:
In[1]:=
Click for copyable input
Out[1]=
 
Find the quarter-way value (lower quartile) of a list:
In[1]:=
Click for copyable input
Out[1]=
 
Lower and upper quartiles:
In[1]:=
Click for copyable input
Out[1]=
 
The q^(th) quantile for a normal distribution:
In[1]:=
Click for copyable input
Out[1]=
New in 5 | Last modified in 6
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team