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Standard Deviation Calculator
Standard Deviation
โ
(sample)
Variance
โ
(ฯยฒ)
Mean
โ
Count
0
Sum
โ
Normal Distribution Ranges
68% of data (ยฑ1 SD) โ to โ
95% of data (ยฑ2 SD) โ to โ
99.7% of data (ยฑ3 SD) โ to โ
Formula
ฯ = โ[ฮฃ(x - ฮผ)ยฒ / n]
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How to Use the Calculator
- Enter your numbers separated by commas, spaces, or new lines
- Choose Sample (for a subset) or Population (for complete data)
- View the standard deviation and variance
- See the normal distribution ranges
When to Use Standard Deviation
- Quality control - Measure consistency in manufacturing
- Finance - Measure investment volatility (risk)
- Research - Describe data spread in experiments
- Grading - Curve grades using mean and SD
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Frequently Asked Questions
What is standard deviation?
Standard deviation measures how spread out numbers are from the mean. A low SD means data points are close to the mean; a high SD means they're spread out.
What's the difference between population and sample SD?
Population SD divides by n (total count). Sample SD divides by n-1 to correct for bias when estimating from a sample. Use sample when you have a subset of data.
What is variance?
Variance is the average of squared deviations from the mean. Standard deviation is the square root of variance, making it in the same units as the data.
How do I interpret standard deviation?
For normal distributions: ~68% of data falls within 1 SD, ~95% within 2 SD, and ~99.7% within 3 SD of the mean.