standard deviation

example.scala

val xs = List(1, 2, 3, 4, 5)
val μ = mean(xs)
val σ = stddev(xs, μ)

stddev.scala

// http://en.wikipedia.org/wiki/Standard_deviation#Basic_examples

def mean(xs: List[Int]): Double = xs match {
  case Nil => 0.0
  case ys => ys.reduceLeft(_ + _) / ys.size.toDouble
}

def stddev(xs: List[Int], avg: Double): Double = xs match {
  case Nil => 0.0
  case ys => math.sqrt((0.0 /: ys) {
   (a,e) => a + math.pow(e - avg, 2.0)
  } / xs.size)
}

Mean should read:

def mean(xs: List[Int]): Double = xs match {
  case Nil => 0.0
  case ys => ys.reduceLeft(_ + _) / ys.size.toDouble
}

mean of Nil and List() is undefined rather than 0.0. Also stddev of Nil, List() and List(Any()) are undefined rather than 0.0. Perhaps the return type should be Option? Or Double.NaN for the "problem" cases?