Standard Deviation Calculator
Calculate standard deviation and statistics
Data Input
Tips:
- • Enter numbers separated by commas
- • Decimals are supported
- • Use sample mode for sample data
- • Population mode for complete data
Results
1.5811
Standard Deviation
Basic Statistics:
Mean:3.0000
Median:3.0000
Mode:1, 2.0, 3.00, 4.000, 5.0000
Range:4.0000
Variance:2.5000
Advanced Statistics:
Skewness:0.0000
Kurtosis:-1.2000
Confidence Intervals:
68% Confidence Interval
1.4189 to 4.5811
95% Confidence Interval
-0.1623 to 6.1623
99% Confidence Interval
-1.7434 to 7.7434
Understanding Standard Deviation
What is Standard Deviation?
Standard deviation measures the amount of variation in a dataset. It indicates how far a set of numbers spreads out from their average value (mean).
- • Small SD: Data clusters near the mean
- • Large SD: Data spreads far from mean
- • Units match original data
- • Always non-negative
Sample vs Population
- • Population: Complete dataset (n)
- • Sample: Subset of population (n-1)
- • Sample SD slightly larger
- • Use sample for estimates
Applications
Science
- • Experimental error
- • Quality control
- • Natural variation
- • Measurement precision
Finance
- • Investment risk
- • Market volatility
- • Portfolio analysis
- • Performance metrics
Education
- • Test score analysis
- • Grade distribution
- • Performance metrics
- • Research analysis