# How to calculate variance

How to calculate variance on the elements of an Array

On Dec 4, 2007 8:56 AM, Surjit N. [email protected]
wrote:

How to calculate variance on the elements of an Array

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

1. iterate over each element and calculate the mean of the elements of
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 5 Dec 2007, at 00:56, Surjit N. wrote:

How to calculate variance on the elements of an Array

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 G.

Bioinformatics Center
Kyoto University

On Dec 4, 2007 5:51 PM, Tim P. [email protected] wrote:

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

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 )

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-