[ S_xx = \sum_i=1^n (x_i - \barx)^2 ]
x = [2,4,6,8]
n = len(x)
sum_x = sum(x)
sum_x2 = sum( xi**2 for xi in x )
Sxx = sum_x2 - (sum_x**2)/n
print(Sxx) # 20.0
This method follows the logic of "calculate the mean, find differences, square them."
$$S_xx = \sum (x_i - \barx)^2$$
Let’s start with a dataset: ( x_1, x_2, x_3, ..., x_n ). Sxx Variance Formula
The mean of these values is: [ \barx = \frac1n \sum_i=1^n x_i ]
The Sxx (often written as ( S_xx ) or ( SS_xx )) is defined as:
[ \boxedS_xx = \sum_i=1^n (x_i - \barx)^2 ] [ S_xx = \sum_i=1^n (x_i - \barx)^2 ]
This formula takes each observation, subtracts the mean (giving the deviation), squares it, and sums across all observations. Because it uses the mean, Sxx is called the "corrected" sum of squares (as opposed to the raw sum of squares, ( \sum x_i^2 )).
In the world of statistics, certain quantities act as the silent workhorses behind the scenes. One such workhorse is Sxx. If you have ever calculated a correlation coefficient, determined the slope of a regression line, or computed a standard error, you have unknowingly used Sxx.
But what exactly is Sxx? Why does it appear in so many critical formulas? And how does it relate to variance? This method follows the logic of "calculate the
This feature breaks down the Sxx variance formula—from its algebraic definition to its intuitive meaning, and from hand calculations to its role in R-squared and hypothesis testing. By the end, you will not just compute Sxx; you will understand it.
This is where the term "Variance Formula" comes into play. $S_xx$ is the "uncorrected" sum of squares. To get the actual Sample Variance ($s^2$), you must divide by $n-1$.
$$s^2 = \fracS_xxn - 1$$
Using our previous example where $S_xx = 8$ and $n = 3$: $$s^2 = \frac83 - 1 = \frac82 = 4$$
Summary of Differences: