Standard Deviation Calculator

    Calculate standard deviation and variance for your dataset

    Standard Deviation Calculator

    Choose "Sample" if your data represents a sample from a larger population. Choose "Population" if your data represents the entire population.

    About Standard Deviation

    Standard deviation measures how spread out data points are from the mean. A low standard deviation indicates data points are close to the mean, while a high standard deviation indicates data points are spread out over a wider range.

    •Formulas

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

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

    Variance:σ² or s² (standard deviation squared)

    •Sample vs Population

    –
    Sample:Uses n-1 (Bessel's correction) for unbiased estimation
    –
    Population:Uses n when you have data for the entire population

    •Features

    • –Calculate both sample and population standard deviation
    • –Shows variance, mean, and other statistics
    • –High precision calculations
    • –Flexible input format
    • –Clear explanations of when to use each method

    •How to Use

    1. 1.Enter your numbers separated by commas, spaces, or new lines
    2. 2.Choose whether your data is a sample or entire population
    3. 3.Click "Calculate Standard Deviation" to get results
    4. 4.View standard deviation, variance, mean, and other statistics

    •Interpretation

    • –Small standard deviation: Data points are close to the mean
    • –Large standard deviation: Data points are spread out
    • –Standard deviation = 0: All data points are identical

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