# (lispkit math stats)

Last updated

Last updated

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.

**(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****)**
**(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****)**
**(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****)**
**(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****)**
**(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)`

.

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.

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.

Computes the median for a set of numbers *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.

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.

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*.

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*.

**(quantile ****xs p****)**

**(percentile ****xs pct****)**

**(median ****xs****)**

**(interquartile-range ****xs****)**

**(five-number-summary ****xs****)**

**(covariance ****xs ys****)**
**(covariance ****xs ys bias****)**

**(correlation ****xs ys****)**
**(correlation ****xs ys bias****)**