#!/usr/bin/env python2
import math

# An imaginary dataset of 50 respondents graded from 1-9, so we have an example to play with:
dataset = [1,1,1,2,3,1,1,4,4,5,6,1,4,9,9,7,7,6,7,5,4,3,6,8,9,5,5,6,6,6,5,5,5,5,4,4,4,6,6,4,7,3,7,3,7,4,4,4,4,9]
# Amounts of each: 1*6,2*1,3*4,4*12,5*8,6*8,7*6,8*1,9*4
# Control: 6+1+4+12+8+8+6+1+4=50

# the mean average (the arithmetic mean) is the sum of all the grades added together, divided by the amount of grades given
mean = sum(dataset)/len(dataset)

# the deviation is calculated as (grade-mean)^2 for each grade in the dataset
deviation = [ (grade-mean)**2 for grade in dataset ]

# the variance is simply the mean of the deviations
variance = sum(deviation)/len(deviation)

# lastly, the standard deviation is the square root of the variance
standard_deviation = math.sqrt(variance)

print (standard_deviation)

# You can now use the standard deviation in the integration of Gaussian distributions