# (lispkit math stats)
Library `(lispkit math stats)` implements statistical utility functions. The functions compute summary values for collections of samples, and functions for managing sequences of samples. Most of the functions accept a list of real numbers corresponding to sample values.
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**(mode *****xs*****)** 
Computes the mode of a set of numbers *xs*. The mode is the value that appears most often in *xs*. *xs* is a proper list of numeric values. `=` is used as the equality operator.
**(mean *****xs*****)**
Computes the arithmetic mean of a set of numbers *xs*. *xs* is a proper list of numeric values.
**(range *****xs*****)**
Computes the range of a set of numbers *xs*, i.e. the difference between the largest and the smallest value. *xs* is a proper list of numeric values which are ordered using the `<` relation.
**(variance *****xs*****)** \
\&#xNAN;**(variance *****xs bias*****)**
Computes the variance for a set of numbers *xs*, optionally applying bias correction. *xs* is a proper list of numeric values. Bias correction gets enabled by setting *bias* to `#t`. Alternatively, it is possible to provide a positive integer, which is used instead of the number of elements in *xs*.
**(stddev *****xs*****)** \
\&#xNAN;**(stddev *****xs bias*****)**
Computes the standard deviation for a set of numbers *xs*, optionally applying bias correction. *xs* is a proper list of numeric values. Bias correction gets enabled by setting *bias* to `#t`. Alternatively, it is possible to provide a positive integer, which is used instead of the number of elements in *xs*.
**(skewness *****xs*****)** \
\&#xNAN;**(skewness *****xs bias*****)**
Computes the skewness for a set of numbers *xs*, optionally applying bias correction. *xs* is a proper list of numeric values. Bias correction gets enabled by setting *bias* to `#t`. Alternatively, it is possible to provide a positive integer, which is used instead of the number of elements in *xs*.
**(kurtosis *****xs*****)** \
\&#xNAN;**(kurtosis *****xs bias*****)**
Computes the kurtosis for a set of numbers *xs*, optionally applying bias correction. *xs* is a proper list of numeric values. Bias correction gets enabled by setting *bias* to `#t`. Alternatively, it is possible to provide a positive integer, which is used instead of the number of elements in *xs*.
**(absdev *****xs*****)**
Computes the average absolute difference between the numbers in list *xs* and `(median xs)`.
**(quantile *****xs p*****)**
Computes the p-quantile for a set of numbers *xs* (also known as the *inverse cumulative distribution*). *p* is a real number between 0 and 1.0. For instance, the 0.5-quantile corresponds to the median.
**(percentile *****xs pct*****)**
Computes the percentile for a set of numbers *xs* and a given percentage *pct*. *pct* is a number between 0 and 100. For instance, the 90th percentile corresponds to the 0.9-quantile.
**(median *****xs*****)**
Computes the median for a set of numbers *xs*.
**(interquartile-range *****xs*****)**
Returns the interquartile range for a given set of numbers *xs*. *xs* is a proper list of numeric values. The interquartile range is the difference between the 0.75-quantile and the 0.25-quantile.
**(five-number-summary *****xs*****)**
Returns a list of 5 statistics describing the set of numbers *xs*: the minimum value, the lower quartile, the median, the upper quartile, and the maximum value.
**(covariance *****xs ys*****)** \
\&#xNAN;**(covariance *****xs ys bias*****)**
Computes the covariance of two sets of numbers *xs* and *ys*. Both *xs* and *ys* are proper lists of numbers. Bias correction can be enabled by setting *bias* to `#t`. Alternatively, it is possible to provide a positive integer, which is used instead of the number of elements in *xs*.
**(correlation *****xs ys*****)** \
\&#xNAN;**(correlation *****xs ys bias*****)**
Computes the correlation of two sets of numbers *xs* and *ys* in form of the *Pearson product-moment correlation coefficient*. Both *xs* and *ys* are proper lists of numbers. Bias correction can be enabled by setting *bias* to `#t`. Alternatively, it is possible to provide a positive integer, which is used instead of the number of elements in *xs*.