Standard Deviation Calculator - Free Statistical Tool

Data Input

Understanding Standard Deviation

Standard deviation measures the amount of variation or dispersion in a dataset.

Population Standard Deviation:
σ = √(Σ(x - μ)² / N)

Sample Standard Deviation:
s = √(Σ(x - x̄)² / (n - 1))

Key Concepts:

Population: Complete set of data
Sample: Subset of population
Variance: Square of standard deviation
Mean: Average of all values

Statistical Results

Count (n)

0

Mean (μ)

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Sum

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Sum of Squares

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Population σ

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Sample s

0

Population σ²

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Sample s²

0

Data Distribution

Calculation Steps

1 Enter data in the input field to begin calculation

Applications

Statistics & Research

Data analysis and interpretation
Hypothesis testing
Confidence intervals
Quality control

Finance & Economics

Investment risk assessment
Portfolio volatility
Market analysis
Financial forecasting

Science & Engineering

Experimental data analysis
Measurement uncertainty
Process control
Quality assurance