Standard Deviation Calculator - Complete Statistical Analysis
Calculate standard deviation, variance, mean, median, mode, quartiles, and other statistical measures. Support for both population and sample data with detailed explanations.
Data Input
Population
Use when you have data for the entire population
Sample
Use when you have sample data from a larger population
Data Visualization
Histogram and Box Plot will be displayed here
Enter data and calculate to see visualization
Statistical Analysis
Values outside 1.5 × IQR from Q1 and Q3 are considered outliers:
Measures relative variability:
Statistical Formulas
Used when you have data for the entire population:
Where: σ = standard deviation, μ = mean, N = population size
Used when working with a sample from a larger population:
Where: s = sample standard deviation, x̄ = sample mean, n = sample size
The square of standard deviation:
How to Use the Standard Deviation Calculator
Step 1: Enter Your Data
Input your numbers separated by commas, spaces, or line breaks. You can also use our sample data sets to get started.
Step 2: Choose Population or Sample
Select "Population" if you have data for the entire group, or "Sample" if your data represents a subset of a larger population.
Step 3: Calculate Results
Click the calculate button to get standard deviation, variance, mean, median, mode, and other statistical measures.
Step 4: Analyze Results
Review the comprehensive statistical analysis including outlier detection and coefficient of variation.