The Ruby Way: Solutions and Techniques in Ruby Programming, Second Edition

5.26. Variance and Standard Deviation

The variance of a set of data is a measure of how “spread out” the values are. (Here we do not distinguish between biased and unbiased estimates.) The standard deviation, usually represented by a sigma (σ) is simply the square root of the variance.

data = [2, 3, 2, 2, 3, 4, 5, 5, 4, 3, 4, 1, 2]

def variance(x)
  m = mean(x)
  sum = 0.0
  x.each {|v| sum += (v-m)**2 }
  sum/x.size
end

def sigma(x)
  Math.sqrt(variance(x))
end

puts variance(data)   # 1.461538462
puts sigma(data)      # 1.20894105

Note that the variance function in the preceding code uses the mean function defined earlier.