What is the difference between population and sample standard deviation?

Population standard deviation (σ) is used when your data represents an entire population, dividing the sum of squared deviations by n. Sample standard deviation (s) is used when your data is a sample drawn from a larger population, dividing by n−1 (Bessel's correction) to produce an unbiased estimate.

What does a high standard deviation mean?

A high standard deviation means the data points are spread widely around the mean, indicating high variability. A low standard deviation means the data points are clustered tightly near the mean, indicating consistency. In finance, a high SD represents higher volatility or risk.

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Standard Deviation Calculator

Calculate mean, median, range, variance, and both population and sample standard deviation for any set of numbers.

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Standard Deviation — Measuring Spread in Data

Population vs. Sample Standard Deviation

When your dataset contains the entire population, divide the sum of squared deviations by n (population SD, σ). When your dataset is a sample drawn from a larger population, divide by n − 1 (sample SD, s) — this is called Bessel's Correction and prevents underestimating the true population spread.

Step-by-Step Calculation

Calculate the mean (μ) of your dataset.
Subtract the mean from each value and square each difference: (xᵢ − μ)²
Sum all the squared differences.
Divide by n (population) or n−1 (sample) to get the variance.
Take the square root of the variance to get SD.

Interpreting Your Result

A low SD indicates data points cluster tightly around the mean. A high SD means values are spread widely. SD is used in finance (portfolio volatility), science (experimental error), and quality control (process consistency).