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.. index:: single: statisticsp .. _statisticsp/0:
.. rst-class:: right
protocol
statisticsp
Statistical calculations over a list of numbers protocol.
| Availability:
| logtalk_load(statistics(loader))
| Author: Paulo Moura | Version: 1:4:0 | Date: 2026-02-20
| Compilation flags:
| static
| Dependencies: | (none)
| Remarks: | (none)
| Inherited public predicates: | (none)
.. contents:: :local: :backlinks: top
Public predicates
.. index:: product/2 .. _statisticsp/0::product/2:
product/2 ^^^^^^^^^^^^^
Calculates the product of all list numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| product(List,Product)
| Mode and number of proofs:
| product(+list(number),-number) - zero_or_one
.. index:: sum/2 .. _statisticsp/0::sum/2:
sum/2 ^^^^^^^^^
Calculates the sum of all list numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| sum(List,Sum)
| Mode and number of proofs:
| sum(+list(number),-number) - zero_or_one
.. index:: min/2 .. _statisticsp/0::min/2:
min/2 ^^^^^^^^^
Determines the minimum value in a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| min(List,Minimum)
| Mode and number of proofs:
| min(+list,-number) - zero_or_one
.. index:: max/2 .. _statisticsp/0::max/2:
max/2 ^^^^^^^^^
Determines the list maximum value in a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| max(List,Maximum)
| Mode and number of proofs:
| max(+list,-number) - zero_or_one
.. index:: min_max/3 .. _statisticsp/0::min_max/3:
min_max/3 ^^^^^^^^^^^^^
Determines the minimum and maximum values in a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| min_max(List,Minimum,Maximum)
| Mode and number of proofs:
| min_max(+list(number),-number,-number) - zero_or_one
.. index:: range/2 .. _statisticsp/0::range/2:
range/2 ^^^^^^^^^^^
Range is the length of the smallest interval which contains all the numbers in List. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| range(List,Range)
| Mode and number of proofs:
| range(+list,-number) - zero_or_one
.. index:: arithmetic_mean/2 .. _statisticsp/0::arithmetic_mean/2:
arithmetic_mean/2 ^^^^^^^^^^^^^^^^^^^^^
Calculates the arithmetic mean of a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| arithmetic_mean(List,Mean)
| Mode and number of proofs:
| arithmetic_mean(+list(number),-float) - zero_or_one
.. index:: geometric_mean/2 .. _statisticsp/0::geometric_mean/2:
geometric_mean/2 ^^^^^^^^^^^^^^^^^^^^
Calculates the geometric mean of a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| geometric_mean(List,Mean)
| Mode and number of proofs:
| geometric_mean(+list(number),-float) - zero_or_one
.. index:: harmonic_mean/2 .. _statisticsp/0::harmonic_mean/2:
harmonic_mean/2 ^^^^^^^^^^^^^^^^^^^
Calculates the harmonic mean of a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| harmonic_mean(List,Mean)
| Mode and number of proofs:
| harmonic_mean(+list(number),-float) - zero_or_one
.. index:: weighted_mean/3 .. _statisticsp/0::weighted_mean/3:
weighted_mean/3 ^^^^^^^^^^^^^^^^^^^
Calculates the weighted mean of a list of numbers. Fails if the list is empty or if the two lists have different lengths. Weights are assumed to be non-negative.
| Compilation flags:
| static
| Template:
| weighted_mean(Weights,List,Mean)
| Mode and number of proofs:
| weighted_mean(+list(number),+list(number),-float) - zero_or_one
.. index:: median/2 .. _statisticsp/0::median/2:
median/2 ^^^^^^^^^^^^
Calculates the median of a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| median(List,Median)
| Mode and number of proofs:
| median(+list(number),-float) - zero_or_one
.. index:: modes/2 .. _statisticsp/0::modes/2:
modes/2 ^^^^^^^^^^^
Returns the list of modes of a list of numbers in ascending order. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| modes(List,Modes)
| Mode and number of proofs:
| modes(+list(number),-list(number)) - zero_or_one
.. index:: average_deviation/3 .. _statisticsp/0::average_deviation/3:
average_deviation/3 ^^^^^^^^^^^^^^^^^^^^^^^
Calculates the average absolute deviation of a list of numbers given a central tendency (e.g., mean, median, or mode). Fails if the list is empty.
| Compilation flags:
| static
| Template:
| average_deviation(List,CentralTendency,Deviation)
| Mode and number of proofs:
| average_deviation(+list(number),+float,-float) - zero_or_one
.. index:: mean_deviation/2 .. _statisticsp/0::mean_deviation/2:
mean_deviation/2 ^^^^^^^^^^^^^^^^^^^^
Calculates the mean absolute deviation of a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| mean_deviation(List,Deviation)
| Mode and number of proofs:
| mean_deviation(+list(number),-float) - zero_or_one
.. index:: median_deviation/2 .. _statisticsp/0::median_deviation/2:
median_deviation/2 ^^^^^^^^^^^^^^^^^^^^^^
Calculates the median absolute deviation of a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| median_deviation(List,Deviation)
| Mode and number of proofs:
| median_deviation(+list(number),-float) - zero_or_one
.. index:: standard_deviation/2 .. _statisticsp/0::standard_deviation/2:
standard_deviation/2 ^^^^^^^^^^^^^^^^^^^^^^^^
Calculates the standard deviation of a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| standard_deviation(List,Deviation)
| Mode and number of proofs:
| standard_deviation(+list(number),-float) - zero_or_one
.. index:: coefficient_of_variation/2 .. _statisticsp/0::coefficient_of_variation/2:
coefficient_of_variation/2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Calculates the coefficient of variation of a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| coefficient_of_variation(List,Coefficient)
| Mode and number of proofs:
| coefficient_of_variation(+list(number),-float) - zero_or_one
.. index:: relative_standard_deviation/2 .. _statisticsp/0::relative_standard_deviation/2:
relative_standard_deviation/2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Calculates the relative standard deviation of a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| relative_standard_deviation(List,Percentage)
| Mode and number of proofs:
| relative_standard_deviation(+list(number),-float) - zero_or_one
.. index:: skewness/2 .. _statisticsp/0::skewness/2:
skewness/2 ^^^^^^^^^^^^^^
Calculates the (moment) skewness of a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| skewness(List,Skewness)
| Mode and number of proofs:
| skewness(+list(number),-float) - zero_or_one
.. index:: kurtosis/2 .. _statisticsp/0::kurtosis/2:
kurtosis/2 ^^^^^^^^^^^^^^
Calculates the (excess) kurtosis of a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| kurtosis(List,Kurtosis)
| Mode and number of proofs:
| kurtosis(+list(number),-float) - zero_or_one
.. index:: variance/2 .. _statisticsp/0::variance/2:
variance/2 ^^^^^^^^^^^^^^
Calculates the unbiased variance of a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| variance(List,Variance)
| Mode and number of proofs:
| variance(+list(number),-float) - zero_or_one
.. index:: z_normalization/2 .. _statisticsp/0::z_normalization/2:
z_normalization/2 ^^^^^^^^^^^^^^^^^^^^^
Normalizes a list of number such that for the resulting list the mean of is close to zero and the standard deviation is close to 1. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| z_normalization(List,NormalizedList)
| Mode and number of proofs:
| z_normalization(+list(number),-list(float)) - zero_or_one
.. index:: fractile/3 .. _statisticsp/0::fractile/3:
fractile/3 ^^^^^^^^^^^^^^
Calculates the smallest value in a list of numbers such that the list elements in its fraction P are less or equal to that value (with P in the open interval (0.0, 1.0)). Fails if the list is empty.
| Compilation flags:
| static
| Template:
| fractile(P,List,Fractile)
| Mode and number of proofs:
| fractile(+float,+list(integer),-integer) - zero_or_one
| fractile(+float,+list(float),-float) - zero_or_one
.. index:: percentile/3 .. _statisticsp/0::percentile/3:
percentile/3 ^^^^^^^^^^^^^^^^
Calculates the P-th percentile of a list of numbers (with P in the open interval (0, 100)). Fails if the list is empty.
| Compilation flags:
| static
| Template:
| percentile(P,List,Percentile)
| Mode and number of proofs:
| percentile(+number,+list(number),-number) - zero_or_one
.. index:: quartiles/4 .. _statisticsp/0::quartiles/4:
quartiles/4 ^^^^^^^^^^^^^^^
Calculates the quartiles (Q1, Q2, Q3) of a list of numbers. Q2 is the median. Q1 and Q3 are the medians of the lower and upper halves, respectively. Fails if the list has fewer than two elements.
| Compilation flags:
| static
| Template:
| quartiles(List,Q1,Q2,Q3)
| Mode and number of proofs:
| quartiles(+list(number),-number,-number,-number) - zero_or_one
.. index:: interquartile_range/2 .. _statisticsp/0::interquartile_range/2:
interquartile_range/2 ^^^^^^^^^^^^^^^^^^^^^^^^^
Calculates the interquartile range (Q3 - Q1) of a list of numbers. Fails if the list has fewer than two elements.
| Compilation flags:
| static
| Template:
| interquartile_range(List,IQR)
| Mode and number of proofs:
| interquartile_range(+list(number),-number) - zero_or_one
.. index:: covariance/3 .. _statisticsp/0::covariance/3:
covariance/3 ^^^^^^^^^^^^^^^^
Calculates the covariance of two lists of numbers. Fails if the lists are empty or have different lengths.
| Compilation flags:
| static
| Template:
| covariance(List1,List2,Covariance)
| Mode and number of proofs:
| covariance(+list(number),+list(number),-float) - zero_or_one
.. index:: correlation/3 .. _statisticsp/0::correlation/3:
correlation/3 ^^^^^^^^^^^^^^^^^
Calculates the Pearson correlation coefficient of two lists of numbers. Fails if the lists are empty or have different lengths.
| Compilation flags:
| static
| Template:
| correlation(List1,List2,Correlation)
| Mode and number of proofs:
| correlation(+list(number),+list(number),-float) - zero_or_one
.. index:: rank_correlation/3 .. _statisticsp/0::rank_correlation/3:
rank_correlation/3 ^^^^^^^^^^^^^^^^^^^^^^
Calculates the Spearman rank correlation coefficient of two lists of numbers. Handles ties using average ranks. Fails if the lists are empty or have different lengths.
| Compilation flags:
| static
| Template:
| rank_correlation(List1,List2,Correlation)
| Mode and number of proofs:
| rank_correlation(+list(number),+list(number),-float) - zero_or_one
.. index:: trimmed_mean/3 .. _statisticsp/0::trimmed_mean/3:
trimmed_mean/3 ^^^^^^^^^^^^^^^^^^
Calculates the trimmed mean of a list of numbers by removing a fraction of extreme values from both ends (with the fraction in the half-open interval [0.0, 0.5)). Fails if the list is empty or if too many elements would be trimmed.
| Compilation flags:
| static
| Template:
| trimmed_mean(Fraction,List,Mean)
| Mode and number of proofs:
| trimmed_mean(+float,+list(number),-float) - zero_or_one
.. index:: sum_of_squares/2 .. _statisticsp/0::sum_of_squares/2:
sum_of_squares/2 ^^^^^^^^^^^^^^^^^^^^
Calculates the sum of squared deviations from the arithmetic mean of a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| sum_of_squares(List,Sum)
| Mode and number of proofs:
| sum_of_squares(+list(number),-float) - zero_or_one
.. index:: central_moment/3 .. _statisticsp/0::central_moment/3:
central_moment/3 ^^^^^^^^^^^^^^^^^^^^
Calculates the K-th central moment of a list of numbers. The K-th central moment is the mean of the deviations from the mean raised to the power K (with K > 0). Fails if the list is empty.
| Compilation flags:
| static
| Template:
| central_moment(K,List,Moment)
| Mode and number of proofs:
| central_moment(+positive_integer,+list(number),-float) - zero_or_one
.. index:: min_max_normalization/2 .. _statisticsp/0::min_max_normalization/2:
min_max_normalization/2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^
Normalizes a list of numbers to the interval [0.0, 1.0] using min-max normalization. Fails if the list is empty or if all values are equal.
| Compilation flags:
| static
| Template:
| min_max_normalization(List,NormalizedList)
| Mode and number of proofs:
| min_max_normalization(+list(number),-list(float)) - zero_or_one
.. index:: frequency_distribution/2 .. _statisticsp/0::frequency_distribution/2:
frequency_distribution/2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Computes the frequency distribution of a list of numbers, returning a list of Value-Count pairs in ascending order of value. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| frequency_distribution(List,Distribution)
| Mode and number of proofs:
| frequency_distribution(+list(number),-list(pair(number,integer))) - zero_or_one
.. index:: standard_error/2 .. _statisticsp/0::standard_error/2:
standard_error/2 ^^^^^^^^^^^^^^^^^^^^
Calculates the standard error of the mean of a list of numbers. Fails if the list is empty.
| Compilation flags:
| static
| Template:
| standard_error(List,Error)
| Mode and number of proofs:
| standard_error(+list(number),-float) - zero_or_one
.. index:: mean_squared_error/3 .. _statisticsp/0::mean_squared_error/3:
mean_squared_error/3 ^^^^^^^^^^^^^^^^^^^^^^^^
Calculates the mean squared error between two lists of numbers. Fails if the lists are empty or have different lengths.
| Compilation flags:
| static
| Template:
| mean_squared_error(List1,List2,Error)
| Mode and number of proofs:
| mean_squared_error(+list(number),+list(number),-float) - zero_or_one
.. index:: root_mean_squared_error/3 .. _statisticsp/0::root_mean_squared_error/3:
root_mean_squared_error/3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Calculates the root mean squared error between two lists of numbers. Fails if the lists are empty or have different lengths.
| Compilation flags:
| static
| Template:
| root_mean_squared_error(List1,List2,Error)
| Mode and number of proofs:
| root_mean_squared_error(+list(number),+list(number),-float) - zero_or_one
.. index:: valid/1 .. _statisticsp/0::valid/1:
valid/1 ^^^^^^^^^^^
Term is a closed list of numbers.
| Compilation flags:
| static
| Template:
| valid(Term)
| Mode and number of proofs:
| valid(@nonvar) - zero_or_one
Protected predicates
(none)
Private predicates
(none)
Operators
(none)
.. seealso::
:ref:`statistics <statistics/0>`, :ref:`sample <sample/0>`, :ref:`population <population/0>`