Bignum compatible StdDev

stats.rb

module Enumerable
  def sum
    self.inject(0){|accum, i| accum + i }
  end

  def mean
    self.sum/self.length.to_f
  end

  def sample_variance
    m = self.mean
    sum = self.inject(0){|accum, i| accum +(i-m)**2 }
    sum/(self.length - 1).to_f
  end

  def standard_deviation
    self.sample_variance ** 0.5
  end

  def z(value)
    (self.mean - value).abs/standard_deviation
  end

  def critical_z
    Enumerable.critical_z(self.size)
  end

  def reject_outliers
    cz = self.critical_z
    self.reject { |value| z(value) > cz }
  end

  def reject_outliers!
    cz = self.critical_z
    self.reject! { |value| z(value) > cz }
  end

  def select_outliers
    cz = self.critical_z
    self.select { |value| z(value) > cz }
  end

  @@critical_z_table = {
    3 => 1.15,
    4 => 1.48,
    5 => 1.71,
    6 => 1.89,
    7 => 2.02,
    8 => 2.13,
    9 => 2.21,
    10 => 2.29,
    11 => 2.34,
    12 => 2.41,
    13 => 2.46,
    14 => 2.51,
    15 => 2.55,
    16 => 2.59,
    17 => 2.62,
    18 => 2.65,
    19 => 2.68,
    20 => 2.71,
    21 => 2.73,
    22 => 2.76,
    23 => 2.78,
    24 => 2.80,
    25 => 2.82,
    26 => 2.84,
    27 => 2.86,
    28 => 2.88,
    29 => 2.89,
    30 => 2.91,
    31 => 2.92,
    32 => 2.94,
    33 => 2.95,
    34 => 2.97,
    35 => 2.98,
    36 => 2.99,
    37 => 3.00,
    38 => 3.01,
    39 => 3.03,
    40 => 3.04,
    50 => 3.13,
    60 => 3.20,
    70 => 3.26,
    80 => 3.31,
    90 => 3.35,
    100 => 3.38,
    110 => 3.42,
    120 => 3.44,
    130 => 3.47,
    140 => 3.49
  }

  def self.critical_z(n)
    result = nil
    @@critical_z_table.keys.sort.each do |key|
      break if key > n
      result = @@critical_z_table[key]
    end
    result
  end
end

values = [1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,100,110]
values.reject_outliers
values.select_outliers