1. What is Sample Sum of Squares?

The sample sum of squares (SS) is a measure of the total variability in a dataset. It represents the sum of the squared differences between each observation and the mean of all observations.

2. How Does the Calculator Work?

The calculator uses the sum of squares formula:

Where:

• \( x_i \) — Individual data points
• \( \bar{x} \) — Mean of all data points
• \( \sum \) — Summation over all data points

Explanation: For each value in your dataset, subtract the mean and square the result. Then sum all these squared differences to get the total sum of squares.

3. Importance of Sum of Squares

Details: The sum of squares is fundamental in statistical analyses like ANOVA, regression, and variance calculation. It quantifies the total variation in the data, which is essential for understanding data distributions and testing hypotheses.

4. Using the Calculator

Tips: Enter your numerical values separated by commas (e.g., "5, 7, 8, 9, 11"). The calculator will compute both the mean and the sum of squares for your sample.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between sample SS and population SS?
A: The calculation is the same, but population SS divides by N (population size) while sample SS typically divides by n-1 (sample size minus 1) for variance.

Q2: Can I use this for negative numbers?
A: Yes, the sum of squares works with any real numbers since differences are squared.

Q3: Why square the differences instead of using absolute values?
A: Squaring emphasizes larger differences and makes the math tractable for many statistical methods.

Q4: How is sum of squares related to standard deviation?
A: Sample standard deviation is the square root of (sum of squares divided by n-1).

Q5: What does a sum of squares of zero mean?
A: It means all values in your dataset are identical (no variation).