Calculate the mode & median averages of a Ruby array

I’ve previously disscussed a way to calculate the mean of an array in Ruby. But there are two other averages that you might see, less commonly used, but still useful.

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Calculate a median…

a = [1, 3, 2, 4, 6, 5, 7, 8]

sorted = a.sort # required
#=> [1, 2, 3, 4, 5, 6, 7, 8]
midpoint = a.length / 2 # integer division
#=> 4
if a.length.even?
  # median is mean of two values around the midpoint
  sorted[midpoint-1, 2].sum / 2.0
else
  sorted[midpoint]
end
#=> 4.5

Calculate a mode…

…using Array#tally then sorting:

a = [1, 3, 3, 4, 6, 5, 7, 8]

tallied = a.tally
#=> {1=>1, 3=>2, 4=>1, 6=>1, 5=>1, 7=>1, 8=>1}
top_pair = tallied.sort_by { |_,v| v }.last(2)
#=> [[8, 1], [3, 2]]
if top_pair.size == 1
  top_pair[0][0] # only one element, it is the mode
elsif top_pair[0][1] == top_pair[1][1]
  nil # if count is same, no mode.
else
  top_pair[1][0]
end
#=> 3

Why?

The #tally method was added to Enumerable in Ruby 2.7 so you might see implementations that use inject, which will perform worse.

I compared the performance of using native Ruby methods versus your own implementations when I wrote about calculating the mean.

Anything else?

It’s no doubt a good idea to further encapsulate these calulations into methods.

If you’re doing a lot of this sort of calculation or in a situation where performance is important you should look at the enumerable-statistics gem. It has natively implemented versions of several statistical summary methods mixed into Array and Enumerable.

The implementation in C means these methods are much faster than any version of the algorithm programmed in Ruby.

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