Comprehensive Calculator Guide
This calculator works out the variance, the average squared deviation from the mean, for a sample or population, with the standard deviation and sum of squares. The population variance of 2, 4, 4, 4, 5, 5, 7, 9 is 4; the sample variance of 10, 12, 23, 23, 16, 23, 21, 16 is 27.43.
Variance
σ² = Σ(x − μ)² ÷ N; s² = Σ(x − x̄)² ÷ (n − 1), Bessel’s correction. It is in squared units, so interpret its root, the SD; but variances of independent variables add, which ANOVA and portfolio risk rely on.
How to Use
- Enter the data.
- Choose sample or population.
- Press “Calculate” to see the variance, SD and sum of squares.
Formula Used
σ² = Σ(x − μ)² ÷ N | s² = Σ(x − x̄)² ÷ (n − 1)
Practical Examples
- Example 1
- Population: 4.
- Example 2
- Sample: 27.43.
Important Tips
- Interpret the SD.
- Use sample for partial data.
- Use Σx² − (Σx)²/n by hand.
Common Mistakes to Avoid
- Comparing variance with the mean.
- Dividing a sample by n.
- Not squaring.
Frequently Asked Questions
- What is variance?
- The mean squared deviation.
- Why n − 1?
- To correct a sample’s bias.
- Can it be negative?
- No.