Standard Deviation

stddev.rb

module Enumerable
  def sum(&blk)
    map(&blk).reduce(0) { |sum, element| sum + element }
  end

  def mean
    sum.to_f / size.to_f
  end

  def variance
    _mean = mean
    sum { |x| (x - _mean) ** 2 } / size
  end

  def std_dev
    Math.sqrt variance
  end

  def z_scores
    _mean, _std_dev = mean, std_dev 
    map { |x| (x - _mean) / _std_dev }
  end

  def scale(range)
    set_max, range_max = max, range.max
    map { |x| x / (set_max / range_max) }
  end
end

module StandardDeviation
  DECILE_BINS = [
    -Float::INFINITY,
    -1.208,
    -0.804,
    -0.502,
    -0.205,
     0.0,
     0.206,
     0.503,
     0.805,
     1.209,
     Float::INFINITY
  ]

  def self.decile(z_score)
    DECILE_BINS.each_with_index { |bin, index| return index if z_score < bin }
  end
end

dollars = %w(
 3013393.3
 3214426.6
 4848175.54
 14564528.09
 3755073.93
 715109.27
 17574128.24
 4264381.68
 15371827.25
 201833.49
 309141.95
 857273.75
 6812680.36
 60268.74
 1893672.23
 26301374.45
 630276.71
 2046414.79
 213316.59
 2435571.19
 4279765.58
 453878.13
 3159793.79
 788693.1
 3964048.29
 3827491.3
 3293435.84
).map(&:to_f)

p dollars.z_scores
p dollars.z_scores.map { |v| StandardDeviation.decile(v) }
p [2, 3, 4, 20].scale(1..10)