Reduce

import Prelude hiding (sum, mean)

reduce :: (a -> b -> b) -> b -> [a] -> b
reduce f b [] = b
reduce f b (a:as) = reduce f (f a b) as 

sum = reduce (\ a b -> a + b) 0

count = reduce (\a b -> 1 + b) 0

mean = snd . reduce 
  (\ x (count, mean) ->
    (count + 1, mean + (1 / (count + 1)) * (x - mean))
  )
  (0, 0)

-- produces descriptive statistics :: (count, sum, mean, variance)
stats = reduce 
  (\ x (count, sum, mean, var) ->
    let k = 1 / (count + 1)
        mean' = mean + k * (x - mean)
        ssr' = (count - 1) * var + k * count * (x - mean) * (x - mean)
    in  (count + 1, sum + x, mean', ssr' / (max 1 count))
  )
  (0, 0, 0, 0)

main = do 
    print $ sum [1 .. 10]
    print $ count [1 .. 10]
    print $ mean [1 .. 10]
    print $ stats [1 .. 10]