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.
- iterate over each element and calculate the mean of the elements of
your Array - 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 - 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-