Standard Deviation Calculator
Calculate standard deviation, variance, mean, and other statistical measures for your dataset. Supports both population and sample standard deviation calculations.
Data Input
Quick Presets
Data Summary
Statistical Results
Primary Statistics
Descriptive Statistics
Quartiles & Percentiles
Additional Statistics
Confidence Intervals (95%)
Distribution Analysis
How Standard Deviation Works
Population Standard Deviation (σ)
Formula:
Where:
- σ = population standard deviation
- x = each value in the dataset
- μ = population mean
- N = total number of values
Sample Standard Deviation (s)
Formula:
Where:
- s = sample standard deviation
- x = each value in the sample
- x̄ = sample mean
- n = sample size
Interpreting Standard Deviation
What Standard Deviation Tells Us
68-95-99.7 Rule (Normal Distribution)
Example Calculations
Example 1: Test Scores
Example 2: Heights (cm)
Frequently Asked Questions
When should I use population vs. sample standard deviation?
Use population standard deviation when you have data for the entire population. Use sample standard deviation when you have a sample from a larger population and want to estimate the population's standard deviation.
What's the difference between standard deviation and variance?
Variance is the average of squared differences from the mean, while standard deviation is the square root of variance. Standard deviation is in the same units as your data, making it easier to interpret.
How do outliers affect standard deviation?
Outliers can significantly increase standard deviation because the calculation involves squared differences. Consider identifying and potentially removing outliers for a more representative measure of variability.