# 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

amazing, check out mine post on python sd : http://codinglio.com/how-to-do-standard-deviation-in-python/