Comprehensive Calculator Guide
This calculator works out how far values spread from their mean, for a sample or a population, with the variance, the mean and each value’s deviation. For 2, 4, 4, 4, 5, 5, 7, 9 as a population the SD is 2 around a mean of 5. It is the main measure of spread in statistics.
Steps and choice
Mean, squared deviations, their sum, divide by N (population) or n − 1 (sample), square root. Choose population when you have everyone, sample when your data stand for more. For roughly normal data, 68% lie within one SD, 95% within two.
How to Use
- Enter the data.
- Choose sample or population.
- Press “Calculate” to see the SD, variance, mean and steps.
Formula Used
σ = √(Σ(x − μ)² ÷ N) | s = √(Σ(x − x̄)² ÷ (n − 1))
Practical Examples
- Example 1
- Population: SD 2.
- Example 2
- Sample of marks: SD 11.32.
Important Tips
- Choose the data type carefully.
- Compare with the mean (CV).
- Check outliers.
Common Mistakes to Avoid
- Reporting the variance as the SD.
- Dividing a sample by n.
- Adding unsquared deviations.
Frequently Asked Questions
- What is the SD?
- The typical distance from the mean.
- Sample vs population?
- n − 1 vs N.
- SD and variance?
- SD = √variance.