Standard Deviation Calculator

Calculate sample and population standard deviation, variance, and mean

Data Input

Enter Numbers (separated by commas, spaces, or line breaks):

Sample Standard Deviation (s)

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Mean (μ / x̄)

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Sample Variance (s²)

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Population Variance (σ²)

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Count (N)

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How to Use the Standard Deviation Calculator

Input Dataset: Paste or enter your series of numbers into the input field separated by commas, spaces, or new lines.
Process Calculation: Click “Calculate Standard Deviation” to compute descriptive statistical indicators.
Analyze Results: Review both Sample Standard Deviation ($s$) and Population Standard Deviation ($\sigma$), as well as mean and variance metrics.

Standard Deviation Formulas

1. Mean Formula:

x̄ = ( Σ x_i ) / N

2. Sample Standard Deviation (s):

s = sqrt[ Σ (x_i – x̄)² / (n – 1) ]

3. Population Standard Deviation (σ):

σ = sqrt[ Σ (x_i – μ)² / N ]

Frequently Asked Questions (FAQ)

What is the difference between Sample and Population Standard Deviation?

Sample standard deviation ($s$) is used when your data represents a subset of a larger group, dividing by $n – 1$ (Bessel’s correction). Population standard deviation ($\sigma$) is used when your data encompasses the entire group being studied, dividing by $N$.

What does a high standard deviation mean?

A high standard deviation indicates that data points are spread out widely over a larger range of values, whereas a low standard deviation means data points tend to be close to the mean.

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