Sum of Squares Calculator
Calculate the sum of squared deviations (SS), variance, and standard deviation with step-by-step residual tables. Includes practice datasets for statistics students.
| Index (i) | Value (xi) | Deviation (x − ) | Squared (x − )2 |
|---|
About
Statistical analysis relies heavily on understanding how data points deviate from the mean. The sum of squared deviations, often denoted as SS or SSxx, is the foundational step in calculating variance and standard deviation. It quantifies the total dispersion in a dataset. In regression analysis, minimizing this value is the core principle behind the Method of Least Squares.
Accuracy in this calculation is vital because errors here propagate into every subsequent statistical test, including t-tests and ANOVA. This tool breaks down the calculation into granular steps, showing the specific residual x − for every entry. This transparency helps students and professionals verify outliers and understand the mechanics of dispersion without relying on opaque black-box functions.
Formulas
The total sum of squares is calculated by summing the squared difference between each data point and the mean:
Where the mean is defined as:
Reference Data
| Practice Set | Description | Difficulty | Expected SS |
|---|---|---|---|
| Set A | Uniform low variance (1, 2, 3) | Beginner | 2.0 |
| Set B | Symmetric distribution (2, 4, 6, 8) | Beginner | 20.0 |
| Set C | Standard Normal approx (decimal inputs) | Intermediate | 4.95 |
| Set D | High magnitude, low variance | Intermediate | 50.0 |
| Set E | Linear sequence (10, 20, 30, 40) | Intermediate | 1000.0 |
| Set F | Outlier influence (1, 1, 1, 100) | Advanced | 7350.75 |
| Set G | Negative integers (-5, 0, 5) | Beginner | 50.0 |
| Set H | Scientific notation (1e2, 2e2, 3e2) | Advanced | 20000.0 |
| Set I | Repeating decimals (1/3 approx) | Advanced | 0.0 (if uniform) |
| Set J | Bio-stats sample (Height in cm) | Real-world | Variable |