Comprehensive Calculator Guide
This calculator works out the sum of squared deviations from the mean (SS) and the sum of the squared values Σx². For 3, 5, 7, 9, 11 the mean is 7 and SS = 40. SS is the numerator of variance and the basis of ANOVA and regression.
Sum of squares
By definition, square each deviation and add; the shortcut is Σx² − (Σx)² ÷ n. Divide by n − 1 for the sample variance; ANOVA and regression split SS into explained and residual parts.
How to Use
- Enter the data.
- No need for the mean first.
- Press “Calculate” to see SS, Σx² and the mean.
Formula Used
SS = Σ(x − x̄)² = Σx² − (Σx)² ÷ n
Practical Examples
- Example 1
- 3 to 11: SS 40.
- Example 2
- Marks: SS 896.875.
Important Tips
- Use the shortcut by hand.
- Σx² ≠ (Σx)².
- Round at the end.
Common Mistakes to Avoid
- Confusing SS with Σx².
- Squaring the sum.
- Rounding the mean early.
Frequently Asked Questions
- What is SS?
- The sum of squared deviations.
- And variance?
- SS ÷ (n − 1) or ÷ n.
- Can it be negative?
- No.