Average time of day

gistfile1.txt

def fixme x
  y=x.split(':')
  y[0].to_i + y[1].to_i/60.0 + y[2].to_i/360.0
end
def formatted x
  hh = x.to_i
  mm_pct = (x - hh) * 60
  mm = mm_pct.to_i
  ss_pct = (mm_pct - mm) * 60
  ss = ss_pct.to_i
  "%02d:%02d:%02d" % [hh,mm,ss]
end    
def average x
  sin_total = 0
  cos_total = 0
  x.each do |s|
    y = fixme s 
    arc = (y/24.0) * 2* Math::PI
    sin_total += Math.sin(arc)
    cos_total += Math.cos(arc)
  end
  z = Math.atan2(sin_total, cos_total) 
  time =  12*(z/Math::PI) 
  fixnum = time > 0 ? time : time + 24
  formatted fixnum
end

a = ["21:00:00",  "22:45:00",  "21:35:00", "00:55:00", "20:50:00"]
# 22:10:49 (edited)
puts average a

 
b=["21:00:00", "22:35:00", "23:15:00", "00:00:00", "01:15:00"]
# 23:13:19
puts average b

c =["10:30:00", "12:15:00", "11:25:00", "13:45:00", "09:40:00"]
# 11:30:24
puts average c

d = ["01:00:00", "11:00:00", "12:00:00", "13:00:00", "23:00:00"]
# 11:59:59
puts average d

e = ['01:00:00', '23:00:00']
puts average e

f = ['01:00:00', '11:00:00']
puts average f

g = ['00:00:00', '12:00:00'] #artifact of finite precision Math::PI
puts average g