Sum of Squares Calculator

How to Use This Sum of Squares Calculator

Delete the default example data set.

Enter your set of numbers into the sum of squares calculator. 

Squared deviation score (statistical sum of squares) and the algebraic sum of squares will automatically be calculated.

Your data set should contain numbers separated by commas:

1,5.8,-50.98,18926,7509.6506832

or spaces:

1 5.8 -50.98 18926 7509.6506832

or line breaks:

1
5.8
-50.98
18926
7509.6506832


or a combination of commas, spaces, and line breaks:

1,5.8 -50.98
18926 20.2
7509.6506832


Invalid values (letters, words, symbols, etc.) will automatically be removed from the data.

Statistical Sum of Squares

The statistical sum of squares is the sum of all squared differences between each value and the data set's mean.

Example: 

Data Set = [1,2,3,4,5]

Sum = 15

Count = 5

Mean = 15 / 5 = 3

Statistical Sum of Squares = (1 - 3)² + (2 - 3)² + (3 - 3)² + (4 - 3)² + (5 - 3)² 

= 4 + 1 + 0 + 1 + 4

= 10

In statistics, population variance is the mean of the sum of squares. 

Standard deviation of population data can then be calculated by finding the square root of the variance.

Algebraic Sum of Squares

The algebraic sum of squares is the sum of all squared values in a data set.

Example:

Data Set = [1,2,3,4,5]

Algebraic Sum of Squares = (1)² + (2)² + (3)² + (4)² + (5)² 

= 1 + 4 + 9 +16 +25

= 55