# Sum of Squares Formula

The sum of squares formula is used to calculate the sum of two or more squares in an expression. To describe how well a model represents the data being modelled, the sum of squares formula is used. Also, the sum of squares is the measure of deviation from the data’s mean value. Hence, it is calculated as the total summation of the squares minus the mean.

## Formulas for Sum of Squares

Sum of squares can be calculated using two formulas i.e. by algebra and by the mean. The formula to calculate the sum of the squares of two values are given below,

Sum of Squares Formulas
In Statistics

Sum of Squares:

= Σ(xi + x̄)2

In Algebra

Sum of Squares of Two Values:

= a2 + b2 = (a + b)2 − 2ab

For “n” Terms

Sum of Squares Formula for “n” numbers

= 12 + 22 + 32 ……. n2 = [n(n + 1)(2n + 1)] / 6

• ∑ = sum
• xi = each value in the set
• x̄ = mean
• xi – x̄ = deviation
• (xi – x̄)2 = square of the deviation
• a, b = numbers
• n = number of terms

### Solved Example

Question: What is the value of 42 + 102?

Solution:

The formula for sum of squares is: a2 + b2 = (a + b)2 − 2ab

From the given equation: a=4 and b=10

42 + 102 = (4 + 10)2 − 2(4)(10)

= 196 − 2(40)

= 196 − 80

= 116