simple stats function implementations

Stats.hs

import Data.List

mean x = (sum x) / (fromIntegral $ length x)

med xs = med' $ sort xs

med' [x] = x
med' [x, y] = (x + y) / 2
med' xs = med' $ drop 1 $ take (length xs - 1) xs

mode :: (RealFrac a) => [a] -> [(a, Int)]
mode xs = foldr f [] $ map mf groups
    where
        groups = group $ sort xs

        mf :: [a] -> (a, Int)
        mf = (\x -> (head x, length x))
        f :: Num a => (a, Int) -> [(a, Int)] -> [(a, Int)]
        f (x, n) [] = [(x, n)]
        f (x, n) acc @ ((xa, na):_) =
            if n > na then [(x, n)]
            else if n == na then (x, n):acc
            else acc

range xs = (maximum xs) - (minimum xs)

iqr xs = (quartile 3 xs) - (quartile 1 xs)

quartile n = quartile' n . sort

quartile' :: (RealFrac a) => Int -> [a] -> a
quartile' 0 xs = minimum xs
quartile' 4 xs = maximum xs
quartile' n xs =
    let
        q = (fromIntegral n) / 4 * (fromIntegral $ 1 + length xs) - 1
        idx = (floor q) :: Int
        off =  (q - (fromIntegral idx))
    in ((1 - off) * (xs!!idx) + off * xs!!(idx + 1))

variance :: RealFrac a => [a] -> a
variance xs =
    let
        m = mean xs
        sq x = x * x
    in (/ (fromIntegral $ length xs)) $ sum $ map (sq . (\x -> x - m)) xs

-- sample variance
varianceS:: RealFrac a => [a] -> a
varianceS xs =
    let
        m = mean xs
        sq x = x * x
    in (/ ((fromIntegral $ length xs) -1)) $ sum $ map (sq . (\x -> x - m)) xs

stddev = sqrt . variance

-- sample stddev
stddevS = sqrt . varianceS