Module: Utilities::Statistics

Defined in:
lib/utilities/utilities.rb

Instance Method Summary collapse

Instance Method Details

#first_quartile(already_sorted = false) ⇒ Object Also known as: lower_quartile

Return the first quartile of self



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# File 'lib/utilities/utilities.rb', line 89

def first_quartile( already_sorted = false )
  return nil if size < 4
  a = already_sorted ? self : sort
  a[0..((size / 2) - 1)].extend(Utilities::Statistics).median( true )
end

#frequences ⇒ Object

Calculate the number of occurences for each element of the array



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# File 'lib/utilities/utilities.rb', line 59

def frequences
  inject(Hash.new(0)) { |h, v| h[v] += 1; h }
end

#interquartile_range(already_sorted = false) ⇒ Object

Calculate the interquartile range of self



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# File 'lib/utilities/utilities.rb', line 111

def interquartile_range( already_sorted = false )
  return nil if size < 4
  a = sort_and_extend( already_sorted )
  a.last_quartile - a.first_quartile
end

#last_quartile(already_sorted = false) ⇒ Object Also known as: upper_quartile

Return the last quartile of self



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# File 'lib/utilities/utilities.rb', line 97

def last_quartile( already_sorted = false )
  return nil if size < 4
  a = already_sorted ? self : sort
  a[((size / 2) + 1)..-1].extend(Utilities::Statistics).median( true )
end

#mean ⇒ Object Also known as: average

Calculate the mean of the array, as long as all objects respond to / operator



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# File 'lib/utilities/utilities.rb', line 52

def mean
  a = flatten.compact.to_stat
  (a.size > 0) ? a.sum.to_f / a.size : nil
end

#median(already_sorted = false) ⇒ Object Also known as: second_quartile

Return the median of sorted self



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# File 'lib/utilities/utilities.rb', line 80

def median( already_sorted = false )
  return nil if empty?
  a = sort_and_extend( already_sorted )
  m_pos = size / 2
  size % 2 == 1 ? a[m_pos] : (a[m_pos-1] + a[m_pos]).to_f / 2
end

#midrange(already_sorted = false) ⇒ Object

Return the midrange of sorted self



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# File 'lib/utilities/utilities.rb', line 125

def midrange( already_sorted = false )
  return nil if empty?
  a = sort_and_extend( already_sorted )
  (a.first + a.last) / 2.0
end

#modes ⇒ Object

Return a hash of modes with their corresponding occurences



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# File 'lib/utilities/utilities.rb', line 118

def modes
  fre = frequences
  max = fre.values.max
  fre.select{ |k, f| f == max }
end

#quartiles(already_sorted = false) ⇒ Object

Return an array containing the first, the second and the last quartile of self



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# File 'lib/utilities/utilities.rb', line 105

def quartiles( already_sorted = false )
  a = sort_and_extend( already_sorted )
  [a.first_quartile( true ), a.median( true ), a.last_quartile( true )]
end

#ranks(already_sorted = false) ⇒ Object

Return a new array containing the rank of each value Ex: [1, 2, 2, 8, 9] #=> [0.0, 1.5, 1.5, 3.0, 4.0]



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# File 'lib/utilities/utilities.rb', line 41

def ranks( already_sorted = false )
  a = already_sorted ? self : sort
  map{ |i| (a.index(i) + a.rindex(i)) / 2.0 }
end

#sqrts ⇒ Object

Calculate square roots of each item



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# File 'lib/utilities/utilities.rb', line 47

def sqrts
  map{ |i| i.sqrt }
end

#squares ⇒ Object

Calculate squares of each item



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# File 'lib/utilities/utilities.rb', line 35

def squares
  map{ |i| i**2 }
end

#standard_deviation(population = false) ⇒ Object Also known as: std_dev

Return the (sample|population) standard deviation of self If population is set to true, then we consider the dataset as the complete population Else, we consider the dataset as a sample, so we use the sample standard deviation (size - 1)



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# File 'lib/utilities/utilities.rb', line 73

def standard_deviation( population = false )
  return nil if empty?
  size > 1 ? Math.sqrt( variance( population ) ) : 0.0
end

#statistical_range(already_sorted = false) ⇒ Object

Return the statistical range of sorted self



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# File 'lib/utilities/utilities.rb', line 132

def statistical_range( already_sorted = false )
  return nil if empty?
  a = sort_and_extend( already_sorted )
  (a.last - a.first)
end

#statistics(already_sorted = false) ⇒ Object Also known as: stats

Return all statistics from self in a simple hash



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# File 'lib/utilities/utilities.rb', line 139

def statistics( already_sorted = false )
  sorted = sort_and_extend( already_sorted )
  
  {
    :first => self.first,
    :last => self.last,
    :size => self.size,
    :sum => self.sum,
    :squares => self.squares,
    :sqrts => self.sqrts,
    :min => self.min,
    :max => self.max,
    :mean => self.mean,
    :frequences => self.frequences,
    :variance => self.variance,
    :standard_deviation => self.standard_deviation,
    :population_variance => self.variance(true),
    :population_standard_deviation => self.standard_deviation(true),
    :modes => self.modes,
    
    # Need to be sorted...
    :ranks => sorted.ranks( true ),
    :median => sorted.median( true ),
    :midrange => sorted.midrange( true ),
    :statistical_range => sorted.statistical_range( true ),
    :quartiles => sorted.quartiles( true ),
    :interquartile_range => sorted.interquartile_range( true )
  }
end

#sum ⇒ Object

Add each object of the array to each other in order to get the sum, as long as all objects respond to + operator



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# File 'lib/utilities/utilities.rb', line 30

def sum
  empty? ? 0 : flatten.compact.inject( :+ )
end

#variance(population = false) ⇒ Object

Return the variance of self



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# File 'lib/utilities/utilities.rb', line 64

def variance( population = false )
  return nil if empty?
  m = mean.to_f
  collect{|v| (v - m).square }.to_stats.sum / (size - (population ? 0 : 1))
end