Sum of Squares Calculator

How to Calculate Sum of Squares

The Sum of Squares (SSQ) is a fundamental concept in statistics and data analysis. It measures the total deviation of a set of data points from their mean value. Understanding how to calculate and interpret the Sum of Squares is crucial for various statistical analyses, including variance, standard deviation, and regression analysis.

Formula and Its Meaning

The formula for Sum of Squares is:

\[SSQ = \sum_{i=1}^{n} x_i^2\]

Where:

• \(SSQ\) is the Sum of Squares
• \(x_i\) are the individual values in a dataset
• \(n\) is the number of values in the dataset

This formula calculates the sum of the squared values of each data point. It's important to note that this is different from the sum of squared deviations from the mean, which is used in calculating variance.

Calculation Steps

1. Square each value in the dataset.
2. Sum up all the squared values.

Example Calculation

Let's calculate the Sum of Squares for the dataset: 2, 4, 6, 8

1. Square each value:
   2² = 4
   4² = 16
   6² = 36
   8² = 64
2. Sum up the squared values:
   \(SSQ = 4 + 16 + 36 + 64 = 120\)

Therefore, the Sum of Squares for this dataset is 120.

Visual Representation

This diagram illustrates the Sum of Squares concept. Each bar represents a data point, with its height proportional to the square of its value. The Sum of Squares (120 in this case) is the total area of all these bars combined.