Standard Deviation Calculator
Calculate standard deviation, variance, and other statistical measures for any dataset. Choose between population and sample calculations with detailed step-by-step results.
Data Input & Calculation Type
Population
Complete dataset
Sample
Subset of data
Results
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Standard Deviation
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Variance
How to Use the Standard Deviation Calculator
Standard deviation is a measure of variability that indicates how spread out data points are from the mean (average). Our calculator supports both population and sample standard deviation calculations. Population standard deviation is used when you have data for an entire group, while sample standard deviation is used when your data represents a subset of a larger population. Simply paste your data values, choose the appropriate calculation type, and get comprehensive statistical analysis including variance, mean, range, and a visual representation of your data distribution.
Population Standard Deviation:
σ = √[(Σ(x - μ)²) / N]
Sample Standard Deviation:
s = √[(Σ(x - x̄)²) / (n - 1)]
σ = √[(Σ(x - μ)²) / N]
Sample Standard Deviation:
s = √[(Σ(x - x̄)²) / (n - 1)]
📈 Example Calculation (Population):
Dataset: Monthly sales figures (in thousands)
Values: 45, 52, 48, 61, 55, 49, 63, 58
Step 1: Calculate mean = (45+52+48+61+55+49+63+58) ÷ 8 = 53.875
Step 2: Find squared deviations from mean:
(45-53.875)² + (52-53.875)² + ... = 302.875
Step 3: Population variance = 302.875 ÷ 8 = 37.86
Step 4: Standard deviation = √37.86 = 6.15
Understanding standard deviation helps you assess the consistency and reliability of your data. A smaller standard deviation indicates that data points are clustered close to the mean, suggesting consistency, while a larger standard deviation shows more variability and spread in your data. This measurement is essential in quality control, risk assessment, academic research, and any field where understanding data variability is crucial for making informed decisions.