//
// function to compute the variance of elements of an array:
// average of square(a[i]-average(a)) 
//

// supporting functions
def average(a:Array[Double]) : Double = {
  a.sum / a.length
}
def square(d:Double) : Double = { d*d }

// main function
def variance(a:Array[Double]) : Double = {
  val avg = average(a)
  // val squares = a.map(x => (x-avg)*(x-avg))
  val squares = a.map(x => square(x-avg))
  // squares.foreach(x => println(x))
  average(squares)
}