Descriptive Statistics

(count-unique lst)

returns: a list of pairs where the car and cdr of each pair are the unique values and counts, respectively, of the values in list lst

> (count-unique '(1 2 3 4 2 1))
((1 . 2) (2 . 2) (3 . 1) (4 . 1))
> (count-unique '(1.1 1 2.2 2 1.1 1.1))
((1 . 1) (1.1 . 3) (2 . 1) (2.2 . 1))
> (count-unique '(0.5 1/2 #e0.5 1 1 2))
((1/2 . 3) (1 . 2) (2 . 1))
> (count-unique '("a" "b" "b" "a"))
Exception in (count-unique lst): at least one element of lst is not a real number

(correlation x y method)

returns: correlation coefficient between values in lists x and y; methods available: 'pearson, 'spearman, 'kendall

> (correlation (iota 10) (iota 10) 'pearson)
1.0
> (correlation (iota 10) (map - (iota 10)) 'pearson)
-1.0
> (correlation '(1 2 3 4) '(2 2.01 2.01 2) 'pearson)
0.0
> (define x '(86 97 99 100 101 103 106 110 112 113 86))
> (define y '(2 20 28 27 50 29 7 17 6 12 1))
> (correlation x y 'pearson)
0.15611738363791983
> (correlation x y 'spearman)
0.11389551189455129
> (correlation x y 'kendall)
0.07339758434175737

(cumulative-sum lst)

returns: a list that is the cumulative sum of the values in lst

> (cumulative-sum '(1 2 3 4 5))
(1 3 6 10 15)
> (cumulative-sum '(5 4 3 2 1))
(5 9 12 14 15)

(diff lst)

returns: list of differences (with lag of one) for all elements in lst

> (diff '(1 3 7 13))
(2 4 6)
> (diff '(-10 20 -10))
(30 -30)

(interquartile-range lst [type])

returns: the difference in the 0.25 and 0.75 sample quantiles of the values in lst corresponding to the given type (see quantile for more info on type)

> (interquartile-range '(1 2 3 5 5))
3.3333333333333335
> (interquartile-range '(1 2 3 5 5) 1)
3
> (interquartile-range '(3 7 4 8 9 7) 9)
4.125

(kurtosis lst)

returns: the kurtosis of the values in lst

> (kurtosis '(-10 0 10))
3/2
> (kurtosis '(1 2 2 3 3 3))
51/25

(mean lst)

returns: the arithmetic mean of the values in lst

> (mean '(1 2 3 4 5))
3
> (mean '(-10 0 10))
0
> (exact->inexact (mean '(1 2 3 4 5 150)))
27.5

(median lst)

returns: the median of lst

> (median '(1 2 3 4 5 6))
3.5
> (quantile '(1 2 3 4 5 6) 0.5 7))
3.5

(mode lst)

returns: a list with the values in lst that occur most frequently

> (mode '(1 1 1 2 2 2))
(1 2)
> (mode '(1 2 3 3 4 4 4))
(4)

(quantile lst p [type])

returns: the sample quantile of the values in lst corresponding to the given probability, p, and type

The quantile function follows Hyndman and Fan 1996 who recommend type 8, which is the default in chez-stats. The default in R is type 7.

> (quantile '(1 2 3 4 5 6) 0.5 1)
3
> (quantile '(1 2 3 4 5 6) 0.5 4)
3.0
> (quantile '(1 2 3 4 5 6) 0.5 8)
3.5
> (quantile '(1 2 3 4 5 6) 0.025 7)
1.125

(rank lst [ties-method])

returns: a list of the sample ranks for the values in lst; ties are handled by replacing ranks with 'min (default), 'max, or 'mean

> (rank '(50 20 50 40 30))
(4 1 4 3 2)
> (rank '(50 20 50 40 30) 'min)
(4 1 4 3 2)
> (rank '(50 20 50 40 30) 'max)
(5 1 5 3 2)
> (rank '(50 20 50 40 30) 'mean))
(9/2 1 9/2 3 2)

(rep n lst type)

returns: the appended list formed by repeating the values in lst either n times or n times each; replicates behavior of rep in R

> (rep 3 '(1 2) 'times)
(1 2 1 2 1 2)
> (rep 3 '(1 2) 'each)
(1 1 1 2 2 2)
> (rep 3 '(a b) 'times)
(a b a b a b)
> (rep 3 '((1 2) (a b)) 'times)
((1 2) (a b) (1 2) (a b) (1 2) (a b))
> (rep 3 '((1 2) (a b)) 'each)
((1 2) (1 2) (1 2) (a b) (a b) (a b))

(rle lst)

returns: run length encoding as a list of pairs where the car and cdr of each pair are the values and lengths of the runs, respectively, for the values in list lst

> (rle '(1 1 1 2 1 1))
((1 . 3) (2 . 1) (1 . 2))
> (rle '(2 2 2 5 3 3))
((2 . 3) (5 . 1) (3 . 2))
> (rle '("a" "b" "b" "a"))
Exception in (rle lst): at least one element of lst is not a real number

(sign x)

returns: sign of x

> (sign -3)
-1
> (sign 0)
0
> (sign 7)
1

(skewness lst)

returns: the skewness of the values in lst

> (skewness '(1 2 3 4 5))
0.0
> (skewness '(1 2 2 3 3 3 4 4 4 4))
-0.6

(standard-deviation lst)

returns: the standard deviation of the values in lst

> (standard-deviation '(0 1 2 3 4 5))
1.8708286933869707
> (sqrt (variance '(0 1 2 3 4 5)))
1.8708286933869707

(sum lst)

returns: the sum of the values in lst

For performance, use (apply + lst) to avoid the overhead of the assertions in (sum lst). sum provides the small convenience of allowing to sum across a list of boolean values (using filter and length).

> (sum (iota 10))
45
> (apply + (iota 10))
45
> (sum '(#t #f #t #f #t))
3
> (length (filter (lambda (x) x) '(#t #f #t #f #t)))
3

(unique lst)

returns: a sorted list of the unique values in lst

> (unique '(0.5 #e0.5 1/2 1 1 1 5.2))
(1/2 1 5.2)
> (unique '(0 0 0 1 1 1 2))
(0 1 2)

(variance lst)

returns: the sample variance of the values in lst based on Welford's algorithm

> (variance '(1 10 100 1000))
233840.25
> (variance '(0 1 2 3 4 5))
3.5

(weighted-mean lst weights)

returns: the arithmetic mean of the values in lst weighted by the values in weights

> (weighted-mean '(1 2 3 4 5) '(5 4 3 2 1))
7/3
> (weighted-mean '(1 2 3 4 5) '(2 2 2 2 2))
3
> (mean '(1 2 3 4 5))
3
> (weighted-mean '(1 2 3 4 5) '(2 0 2 2 2))
13/4
> (mean '(1 3 4 5))
13/4