Sum of Squares in Statistics
In statistics, the value of the sum of squares tells the degree of dispersion in a dataset. It evaluates the variance of the data points from the mean and helps for a better understanding of the data. The large value of the sum of squares indicates that there is a high variation of the data points from the mean value, while the small value indicates that there is a low variation of the data from its mean.
The formula used to calculate the sum of squares in Statistics is,
Sum of Squares of n Data points = ∑ni=0 (xi – x̄)2
where,
- ∑ represents Sum of Series
- xi represents each value in Set
- x̄ represents Mean of Values
- (xi – x̄) represents Deviation from Mean Value
- n represents Number of Terms in Series
Sum of Squares
Sum of squares in the addition of the square of the numbers i.e. we find the sum of squares by first finding the individual squares and then adding them to find the sum of the squares. We define the sum of squares in statistics as the variation of the data set. In algebra, we can find the sum of squares for two terms, three terms, or “n” number of terms, etc. We can find the sum of squares of two numbers using the algebraic identity,
- (a + b)2 = a2 + b2 + 2ab
We can also find the sum of squares of more than two terms using the concept of Algebra and Mathematical Induction. In this article, we will learn about the different sum of squares formulas, their examples, proofs, and others in detail.
Table of Content
- What is Sum of Squares?
- Sum of Squares Formula
- Sum of Squares for “n” Natural Numbers
- Sum of Squares in Statistics
- Steps to Find Sum of Squares
- Sum of Squares Error
- Sum of Square Table