Learning Haskell: Combine sample means for multiple experimental runs

combineSummaryStats.hs

import Data.Monoid;

x1 = [1..100]
x2 = [2,4..100]
x3 = [3,6..100]

data Summary = Summary {µ::Float, n::Int} deriving (Show)

instance Monoid Summary where
    mempty = Summary { µ = 0, n = 0 }
    mappend s1 s2 = Summary {
        µ = combinedMean s1 s2,
        n = (n s1) + (n s2)
    }

count :: [Float] -> Int
count xs = length xs

mean :: [Float] -> Float
mean xs =
    let s = sum xs
        n = fromIntegral $ count xs
    in  s / n

describe :: [Float] -> Summary
describe xs = Summary { µ = mean xs, n = count xs }

combinedMean :: Summary -> Summary -> Float
combinedMean s1 s2 =
    let n1 = fromIntegral $ n s1
        n2 = fromIntegral $ n s2
        µ1 = µ s1
        µ2 = µ s2
    in  (µ1 * n1 + µ2 * n2) / (n1 + n2)

main :: IO ()
main = do
    putStrLn $ "          x1 - " ++ (show $ d1)
    putStrLn $ "          x2 - " ++ (show $ d2)
    putStrLn $ "          x3 - " ++ (show $ d3)
    putStrLn $ "     x1 + x2 - " ++ (show $ d1 <> d2)
    putStrLn $ "x1 + x2 + x3 - " ++ (show $ mconcat [d1, d2, d3])
    where
        [d1, d2, d3] = map describe [x1, x2, x3]

Output

          x1 - Summary {µ = 50.5, n = 100}
          x2 - Summary {µ = 51.0, n = 50}
          x3 - Summary {µ = 51.0, n = 33}
     x1 + x2 - Summary {µ = 50.666668, n = 150}
x1 + x2 + x3 - Summary {µ = 50.726776, n = 183}