Average, variance & standard deviation in Python

Here is a quick python script which calculates average, variance and standard deviation. This is also part of codeacademy work. I must say last time I worked with variance and standard deviation it was more than 10 years ago in statistics course. Hence a bit of reminder here for me too: (Some are from wikipedia and mathsisfun.com)

Average: In mathematics and statistics, it is called arithmetic mean according to wikipedia but simply it is the sum of a list of numbers divided by the number of numbers in the list.

Variance: The average of the squared differences from the mean. Here is the formula which we will use in our python code.

Standard deviation: Square root of the variance is the standard deviation which just means how far we are from the normal(mean)

Now here is the code which calculates given the number of scores of students we calculate the average,variance and standard deviation.

grades = [100, 100, 90, 40, 80, 100, 85, 70, 90, 65, 90, 85, 50.5]

#First print the grades
def print_grades(grades):
    for grade in grades:
        print grade

#calculate the sum
def grades_sum(grades):
    total = 0
    for grade in grades: 
        total += grade
    return total

#Take the average by adding up each grade    
def grades_average(grades):
    sum_of_grades = grades_sum(grades)
    average = sum_of_grades / float(len(grades))
    return average

#Here we calculate the variance given the formula above 
#by subtracting each score from the average and then taking square and rolling the sum. 
def grades_variance(scores):
    average = grades_average(scores)
    variance = 0
    for score in scores:
        variance = variance + (average - score) ** 2
    
    return variance/len(scores)

print grades_variance(grades)

#And here the standard deviation comes by taking square root of the variance
def grades_std_deviation(variance):
    return variance ** 0.5
variance = grades_variance(grades)
    
print grades_std_deviation(variance)

See:
http://www.mathsisfun.com/data/standard-deviation.html