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Statistics

All statistical procedures ignore 'na values by default (na-rm defaults to #t). Pass #f to propagate 'na.

Booleans are coerced to numbers: #t → 1, #f → 0.

List utilities

(count obj lst)

returns: the number of occurrences of obj in lst.

(count-elements lst)

returns: a list of (element . count) pairs for every unique element in lst.

(rle lst)

returns: run-length encoding of lst as a list of (element . count) pairs.

(remove-duplicates lst)

returns: lst with duplicate elements removed, preserving first-occurrence order.

(rep lst n type)

returns: lst repeated n times. type must be 'times (repeat the whole list) or 'each (repeat each element).

(transpose lst)

returns: the transposed list-of-lists.

> (define x '(a b b c c c d d d d na))

> (count 'c x)
3

> (count-elements x)
((a . 1) (b . 2) (c . 3) (d . 4) (na . 1))

> (rle '(1 1 2 1 1 0 2 2))
((1 . 2) (2 . 1) (1 . 2) (0 . 1) (2 . 2))

> (remove-duplicates x)
(a b c d na)

> (rep '(1 2) 3 'times)
(1 2 1 2 1 2)

> (rep '(1 2) 3 'each)
(1 1 1 2 2 2)

> (transpose '((1 2 3) (4 5 6)))
((1 4) (2 5) (3 6))

Descriptive statistics

(sum lst [na-rm])

returns: the sum of values in lst.

> (sum (iota 10))
45
> (sum (cons 'na (iota 10)))   ; na-rm defaults to #t
45
> (sum (cons 'na (iota 10)) #f)
na
> (sum '(#t #f #t #f #t))
3

(product lst [na-rm])

returns: the product of values in lst.

> (product (map add1 (iota 10)))
3628800
> (product '(#t #f #t #f #t))
0

(mean lst [na-rm])

returns: the arithmetic mean of values in lst.

> (mean '(1 2 3 4 5))
3
> (mean '(-10 0 10 na) #f)
na
> (mean '(#t #f #t na))
2/3

(weighted-mean lst weights [na-rm])

returns: the weighted arithmetic mean. na-rm applies only to lst; any 'na in weights yields 'na.

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

(variance lst [na-rm])

returns: the sample variance using Welford's algorithm.

> (inexact (variance '(1 10 100 1000)))
233840.25
> (variance '(0 1 2 3 4 5))
7/2

(standard-deviation lst [na-rm])

returns: the sample standard deviation.

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

(median lst [type na-rm])

returns: the median of lst. Uses type 8 by default (see quantile).

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

(quantile lst p [type na-rm])

returns: the sample quantile at probability p. type is an integer 1–9 following Hyndman and Fan (1996); defaults to type 8. R's default is type 7.

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

(interquartile-range lst [type na-rm])

returns: the difference between the 0.75 and 0.25 quantiles. Defaults to type 8.

> (interquartile-range '(1 2 3 5 5))
3.3333333333333335
> (interquartile-range '(1 2 3 5 5) 1)
3

(cumulative-sum lst)

returns: a list of running totals. Propagates 'na once encountered.

> (cumulative-sum '(1 2 3 4 5))
(1 3 6 10 15)
> (cumulative-sum '(1 2 3 na 4))
(1 3 6 na na)