Warren Seen » statistics http://warrenseen.com/blog freelance software developer Wed, 03 Jun 2009 23:54:34 +0000 http://wordpress.org/?v=2.8.4 en hourly 1 Ruby Cheap Tricks – Stats http://warrenseen.com/blog/2007/02/22/ruby-cheap-tricks-stats/ http://warrenseen.com/blog/2007/02/22/ruby-cheap-tricks-stats/#comments Wed, 21 Feb 2007 22:32:01 +0000 warren http://warrenseen.com/blog/2007/02/22/ruby-cheap-tricks-stats/ For when it’s just as quick to roll your own …

Ruby [Show Plain Code]:
  1. # In each of these functions, data is just an array of numbers
  2. # average
  3. def avg(data)
  4.   data.inject(0.0) { |sum, i| sum + i } / data.length
  5. end
  6.  
  7. # median value
  8. def median(data)
  9.   data.sort!
  10.   index = data.length / 2
  11.   (data.length % 2 == 0) ? data[index] : avg(data.values_at(index.floor, index.ceil))
  12. end
  13.  
  14. # interquartile mean
  15. def iqm(data)
  16.   data.sort!
  17.   first = (data.length/4).truncate
  18.   last = 3 * first
  19.   avg(data[first..last])
  20. end

]]> http://warrenseen.com/blog/2007/02/22/ruby-cheap-tricks-stats/feed/ 0 How to calculate standard deviation http://warrenseen.com/blog/2006/03/13/how-to-calculate-standard-deviation/ http://warrenseen.com/blog/2006/03/13/how-to-calculate-standard-deviation/#comments Mon, 13 Mar 2006 08:03:41 +0000 warren http://warrenseen.com/blog/2006/03/13/how-to-calculate-standard-deviation/ When I started this blog last month, I thought “Standard Deviation” was a snappy title. Of course, I also knew about standard deviation as a statistical tool, however I didn’t expect that this overlap would cause Google search to drive 50+ visitors a month here looking for implementations of the standard deviation formula.

So as a “public service”, here is some code to figure standard deviation in Ruby and Java.

(disclaimer: no warranties as to correctness, particularly to the nth decimal place, don’t use this to run your home made nuclear reactor or air traffic control system, blah blah, etc, etc :-) )

The algorithm I’ll be using is “borrowed” from wikipedia’s entry on Algorithms to calculate variance. Specifically, I’ll be using a variant of algorithm II, which is sourced from Knuth, except we’ll calculate the standard deviation for the population, rather than a sample.

As you should probably know, standard deviation is defined as the square root of the variance. If you didn’t know this, maybe you should go read about standard deviation first.

Java [Show Plain Code]:
  1. /**
  2. * @param population an array, the population
  3. * @return the variance
  4. */
  5. public double variance(double[] population) {
  6.         long n = 0;
  7.         double mean = 0;
  8.         double s = 0.0;
  9.  
  10.         for (double x : population) {
  11.                 n++;
  12.                 double delta = x – mean;
  13.                 mean += delta / n;
  14.                 s += delta * (x – mean);
  15.         }
  16.         // if you want to calculate std deviation
  17.         // of a sample change this to (s/(n-1))
  18.         return (s / n);
  19. }
  20.  
  21. /**
  22. * @param population an array, the population
  23. * @return the standard deviation
  24. */
  25. public double standard_deviation(double[] population) {
  26.         return Math.sqrt(variance(population));
  27. }

example usage:

Java [Show Plain Code]:
  1. double[] arr = { 1, 3, 24, 17, 12, 6, 14};
  2. System.out.printf("%f", standard_deviation(arr));
  3.   // prints 7.596992
Ruby [Show Plain Code]:
  1. def variance(population)
  2.     n = 0
  3.     mean = 0.0
  4.     s = 0.0
  5.     population.each { |x|
  6.       n = n + 1
  7.       delta = x – mean
  8.       mean = mean + (delta / n)
  9.       s = s + delta * (x – mean)
  10.     }
  11.     # if you want to calculate std deviation
  12.     # of a sample change this to "s / (n-1)"
  13.     return s / n
  14.   end
  15.  
  16.   # calculate the standard deviation of a population
  17.   # accepts: an array, the population
  18.   # returns: the standard deviation
  19.   def standard_deviation(population)
  20.     Math.sqrt(variance(population))
  21.   end

example usage:

Ruby [Show Plain Code]:
  1. puts standard_deviation([1, 3, 24, 17, 12, 6, 14])
  2.  # prints 7.59699188589047

If you found this at all useful, (or have spotted a bug), please leave a comment to that effect…

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