class SDeviation

		attr_reader :sum,:sumatory,:data,:average,:stddeviation,:strprocedure,:stddeviation_sqrt,:error,:error_size
     
		def initialize(data,error)
				@sum = 0
				@sumatory = 0
				@data = data
				@error = error
				@error_size = @error.to_s.split('.')[1].size
				@average = 0
				@stddeviation = 0
				@strprocedure = ''
		end

		def setError(v)
				d = v-v.to_i
				r = (d*10**(@error_size-1)-(d*10**(@error_size-1)).to_i)*10**-(@error_size-1)
				rounded = ((r*(10**(@error_size-1))).round)*10**-(@error_size-1)
				return v-r+rounded
		end
	
		def Average
				@strprocedure = "$\\overline{x}=\\frac{\\sum_{i=1}^n x_i}{n}$\\\\\n"
				@strprocedure += "$\\overline{x}=\\frac{\\sum_{i=1}^{#{@data.size}} x_i}{#{@data.size}}$\\\\\n"
				@strprocedure += "$\\overline{x}=\\frac{"
				@data.each do |e| 
						@sum += e
						@strprocedure += "#{e}+"
				end
				@strprocedure = @strprocedure[0..-2]
				@average = setError(@sum / @data.size.to_f)
				@strprocedure += "}{#{@data.size}}$\\\\\n"
		end
	
		def Sumatory
				@strprocedure += "$\\sum_{i=1}^n (x_i-\\overline{x})^2$\\\\\n"
				@strprocedure += "$\\sum_{i=1}^{#{@data.size}} (x_i-\\overline{x})^2=$\\\\\n"
				@strprocedure += "$"
				@data.each do |e| 
						@sumatory += setError((e-@average)**2)
						@strprocedure += "(#{e}-#{@average})^2+"
				end
				@strprocedure = @strprocedure[0..-2]
				@strprocedure += "$\\\\\n"
				@strprocedure += "$=#{@sumatory}$\\\\\n"
		end
	
		def StdDeviation
				@stddeviation = setError(@sumatory / (@data.size.to_f - 1))
				@stddeviation_sqrt = setError(Math::sqrt(@stddeviation))
				@strprocedure += "$\\sigma^2 = \\frac{\\sum_{i=1}^n (x_i-\\overline{x})^2}{n-1}$\\\\\n"
				@strprocedure += "$\\sigma^2 = \\frac{\\sum_{i=1}^{#{@data.size}} (x_i-\\overline{x})^2}{#{@data.size}-1}$\\\\\n"
				@strprocedure += "$\\sigma^2 = \\frac{#{@sumatory}}{#{@data.size-1}}$\\\\\n"
				@strprocedure += "$\\sigma^2 = #{@stddeviation}$\\\\\n"
				@strprocedure += "$\\sigma = #{@stddeviation_sqrt}$\\\\\n"
		end
	
end