Total Sum of Squares (TSS) in python

Question

I'm trying to calculate the total sum of squares using python. I know that the formula of TSS is: [enter image description here][1]

I created a code to do it:

from statistics import mean

x = ([3,1,3,1,3,13])

def tss(a):
    m = mean(a)
    for i in a:
        i += ((i-m)**2)
    return (i) 

print(tss(x))

The problem is: Its keeping returning me 94, but i know that the correct answer is 102. I don't have a clue of what i did wrong. Can anybody help me? [1]: https://i.stack.imgur.com/Alx6r.png

Answer 1

i is resetting each time it goes through the loop. So on the last loop your function erases all the previous sums, sets i to 13, then adds the square of the difference between 13 and the mean to i (which is now 13), returning 94. You need a different variable to track the sum, so it doesn't get lost each loop. You want:

from statistics import mean

x = ([3,1,3,1,3,13])

def tss(a):
    m = mean(a)
    n = 0
    for i in a:
        n += ((i-m)**2)
    return (n)

print(tss(x))
'''

@mateen's answer is more pythonic and will perform better than a loop, but I don't think you'll get the understanding from it. Welcome to python!

Answer 2

Without numpy:

def tss(xs):
    m = sum(xs) / len(xs)
    return sum((x - m)**2 for x in xs)

With numpy:

import numpy as np

def tss(x):
    return ((x - np.mean(x))**2).sum()

Answer 3

If you want to keep your initial script , just do :

from statistics import mean

x = ([3, 1, 3, 1, 3, 13])

def tss(a):
    total = 0
    for i in a:
        total = total + ((i-mean(a))**2)
    return total