Grouping numbers for a histogram

Question

I have a bunch of numbers I want to use to generate a histogram for a standard score.

Therefore I compute the mean and the standard deviation of the numbers and normalize each x with this formula

x' = (x-mean)/std_dev

The result is a number between -4 and 4. I want to chart that result. I am looking for a way to group the numbers in order to avoid to small bars.

My plan is to have bins in the interval [-4,4] centered at consecutavice quarter units, i.e [-4,-3.75,...,3.75,4]

Example: 0.1 => bin "0.0", 0.3 => bin "0.25", -1.3 => Bin "-1.5"

What is the best way to achieve that?

Answer 1

Rails provides Enumerable#group_by -- see source here, assuming you're not using Rails: http://api.rubyonrails.org/classes/Enumerable.html

Assuming your list is called xs, you could do something like the following (untested):

bars = xs.group_by {|x| #determine bin here}

Then you'll have a hash that looks like:

bars = { 0 => [elements,in,first,bin], 1 => [elements,in,second,bin], etc }

Answer 2

Here's a solution that doesn't use any third part libraries. The numbers should be in the Array vals.

MULTIPLIER  = 0.25 
multipliers = []
0.step(1, MULTIPLIER) { |n| multipliers << n }

histogram = Hash.new 0

# find the appropriate "bin" and create the histogram
vals.each do |val|
  # create an array with all the residuals and select the smallest
  cmp = multipliers.map { |group| [group, (group - val%1).abs] }
  bin = cmp.min { |a, b| a.last <=> b.last }.first
  histogram[val.truncate + bin] += 1
end

I think that it performs the proper rounding. But I only tried it with:

vals = Array.new(10000) { (rand * 10) % 4 * (rand(2) == 0 ? 1 : -1) }

and the distribution got kind of skewed, but that's probably the random number generator's fault.