How can I do standard deviation in Ruby?

Question

I have several records with a given attribute, and I want to find the standard deviation.

How do I do that?

Answer 1

It appears that Angela may have been wanting an existing library. After playing with statsample, array-statisics, and a few others, I'd recommend the descriptive_statistics gem if you're trying to avoid reinventing the wheel.

gem install descriptive_statistics

$ irb
1.9.2 :001 > require 'descriptive_statistics'
 => true 
1.9.2 :002 > samples = [1, 2, 2.2, 2.3, 4, 5]
 => [1, 2, 2.2, 2.3, 4, 5] 
1.9.2p290 :003 > samples.sum
 => 16.5 
1.9.2 :004 > samples.mean
 => 2.75 
1.9.2 :005 > samples.variance
 => 1.7924999999999998 
1.9.2 :006 > samples.standard_deviation
 => 1.3388427838995882 

I can't speak to its statistical correctness, or your comfort with monkey-patching Enumerable; but it's easy to use and easy to contribute to.

Answer 2

If the records at hand are of type Integer or Rational, you may want to compute the variance using Rational instead of Float to avoid errors introduced by rounding.

For example:

def variance(list)
  mean = list.reduce(:+)/list.length.to_r
  sum_of_squared_differences = list.map { |i| (i - mean)**2 }.reduce(:+)
  sum_of_squared_differences/list.length
end

(It would be prudent to add special-case handling for empty lists and other edge cases.)

Then the square root can be defined as:

def std_dev(list)
  Math.sqrt(variance(list))
end

Answer 3

I'm not a big fan of adding methods to Enumerable since there could be unwanted side effects. It also gives methods really specific to an array of numbers to any class inheriting from Enumerable, which doesn't make sense in most cases.

While this is fine for tests, scripts or small apps, it's risky for larger applications, so here's an alternative based on @tolitius' answer which was already perfect. This is more for reference than anything else:

module MyApp::Maths
  def self.sum(a)
    a.inject(0){ |accum, i| accum + i }
  end

  def self.mean(a)
    sum(a) / a.length.to_f
  end

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

  def self.standard_deviation(a)
    Math.sqrt(sample_variance(a))
  end
end

And then you use it as such:

2.0.0p353 > MyApp::Maths.standard_deviation([1,2,3,4,5])
=> 1.5811388300841898

2.0.0p353 :007 > a = [ 20, 23, 23, 24, 25, 22, 12, 21, 29 ]
 => [20, 23, 23, 24, 25, 22, 12, 21, 29]

2.0.0p353 :008 > MyApp::Maths.standard_deviation(a)
 => 4.594682917363407

2.0.0p353 :043 > MyApp::Maths.standard_deviation([1,2,2.2,2.3,4,5])
 => 1.466628787389638

The behavior is the same, but it avoids the overheads and risks of adding methods to Enumerable.

Answer 4

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
      Math.sqrt(self.sample_variance)
    end

end 

Testing it:

a = [ 20, 23, 23, 24, 25, 22, 12, 21, 29 ]
a.standard_deviation  
# => 4.594682917363407

---

01/17/2012:

fixing "sample_variance" thanks to Dave Sag

Answer 5

Or how about:

class Stats
    def initialize( a )
        @avg = a.count > 0 ? a.sum / a.count.to_f : 0.0
        @stdev = a.count > 0 ? ( a.reduce(0){ |sum, v| sum + (@avg - v) ** 2 } / a.count ) ** 0.5 : 0.0
    end
end

Answer 6

As a simple function, given a list of numbers:

def standard_deviation(list)
  mean = list.inject(:+) / list.length.to_f
  var_sum = list.map{|n| (n-mean)**2}.inject(:+).to_f
  sample_variance = var_sum / (list.length - 1)
  Math.sqrt(sample_variance)
end