How to calculate variance

ruby-talk
1

How to calculate variance on the elements of an Array

···

--
Posted via http://www.ruby-forum.com/.

2

Implement this algorithm <http://mathworld.wolfram.com/Variance.html>.

1) iterate over each element and calculate the mean of the elements of
your Array
2) iterate again over each element and take the difference of each
element with the mean, square that value, and then add it to a running
total
3) that running total is your variance

ary = (1..100).to_a
mean = (ary.inject(0.0) {|s,x| s + x}) / Float(ary.length)
variance = ary.inject(0.0) {|s,x| s + (x - mean)**2}

Another option is to install the NArray library and use that ...

nary = NArray.new(NArray::FLOAT, 100)
nary[0...100] = (1..100).to_a
nary.variance

Blessings,
TwP

···

On Dec 4, 2007 8:56 AM, Surjit Nameirakpam <surjit.meitei@gmail.com> wrote:

How to calculate variance on the elements of an Array

3

*Shameless plug and probably overkill if you just want the variance*

RSRuby allows you to use any R function, including the built-in variance function ('var'). It's available as a gem.

irb(main):002:0> require 'rsruby'
=> true
irb(main):004:0> RSRuby.instance.var([1,2,3])
=> 1.0
irb(main):006:0> RSRuby.instance.var(RSRuby.instance.rnorm(10))
=> 0.812117410016217
irb(main):008:0> RSRuby.instance.var(RSRuby.instance.rnorm(100))
=> 0.960224242747171

Alex Gutteridge

Bioinformatics Center
Kyoto University

···

On 5 Dec 2007, at 00:56, Surjit Nameirakpam wrote:

How to calculate variance on the elements of an Array

4

You can also write this, if you are going to need it in more places,
in a more generic way:

module Variance

  def sum(&blk)
    map(&blk).inject { |sum, element| sum + element }
  end

  def mean
    (sum.to_f / size.to_f)
  end

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

  def std_dev
    Math.sqrt(variance)
  end
end

Array.send :include, Variance

puts [1, 2].sum # 3
puts [1, 2].mean # 1.5
puts [1, 2].variance # 0.25
puts [1, 2].std_dev # 0.5

Longer but nicer (maybe :wink: )

···

On Dec 4, 2007 5:51 PM, Tim Pease <tim.pease@gmail.com> wrote:

Implement this algorithm <http://mathworld.wolfram.com/Variance.html>.

1) iterate over each element and calculate the mean of the elements of
your Array
2) iterate again over each element and take the difference of each
element with the mean, square that value, and then add it to a running
total
3) that running total is your variance

ary = (1..100).to_a
mean = (ary.inject(0.0) {|s,x| s + x}) / Float(ary.length)
variance = ary.inject(0.0) {|s,x| s + (x - mean)**2}

--
Sergio Gil Pérez de la Manga
e-mail > sgilperez@gmail.com
blog > http://www.lacoctelera.com/porras

5

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

If you wanted it to be a little more efficient you can do it like so:

def variance( arr )
  n, mean, s = [0, 0, 0]

  arr.each_with_index do |x, n|
    delta = (x - mean).to_f
    mean += delta/(n+1)
    s += delta*(x - mean)
  end

  s/n
end

It calculates the variance in one pass by calculating the mean and
variance iteratively [1].

-rr-

[1] http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance