What is the difference between population and sample standard deviation?

Population standard deviation uses data from the entire group, while sample standard deviation uses Bessel's correction (dividing by n-1) to estimate the population variability from a subset.

Why do we use n-1 in the sample standard deviation formula?

Using n-1, known as Bessel's correction, corrects the bias in the estimation of the population variance and standard deviation from a sample.

When should I use the population standard deviation formula?

Use the population standard deviation formula when you have data for the entire population and want to measure its variability precisely.

Why Are There Two Standard Deviation Formulas: Population vs Sample Explained

Learn why standard deviation has two formulas—one for populations and one for samples using Bessel's correction for unbiased estimates.

198 views

Jun 11, 2026

Population vs. Sample: Standard deviation has two formulas because one is used for an entire population (σ), and the other is for a sample (s). The sample formula uses n-1 (Bessel's correction) to provide an unbiased estimate of the population standard deviation.

FAQs & Answers

What is the difference between population and sample standard deviation? Population standard deviation uses data from the entire group, while sample standard deviation uses Bessel's correction (dividing by n-1) to estimate the population variability from a subset.
Why do we use n-1 in the sample standard deviation formula? Using n-1, known as Bessel's correction, corrects the bias in the estimation of the population variance and standard deviation from a sample.
When should I use the population standard deviation formula? Use the population standard deviation formula when you have data for the entire population and want to measure its variability precisely.

Watch More

For a deeper understanding of statistical measures, explore our related videos on variance calculation, understanding statistical bias, and applying standard deviation in data analysis.

Why Are There Two Different Standard Deviation Formulas for Sample and Population? Learn why two standard deviation formulas exist and how they differ to accurately measure variability in samples versus populations.
Why Are There Two Different Formulas for Standard Deviation? Learn why standard deviation formulas differ for populations and samples, and how to choose the right one for accurate statistics.
How to Calculate Standard Deviation: Population vs Sample Methods Explained Learn the two methods to calculate standard deviation—population and sample—and how to apply each formula correctly.
Why Are There Two Types of Standard Deviation? Explained Learn why two types of standard deviation exist and how population and sample standard deviations differ in measuring data variability.
Is Standard Deviation Represented by S or σ? Understanding the Difference Learn whether standard deviation is denoted by σ or S and how it varies between population and sample data sets.
Which Standard Deviation Should I Use: Population vs Sample Explained Learn when to use population standard deviation versus sample standard deviation in statistics and research for accurate data analysis.
What Is the Difference Between Sigma (σ) and Standard Deviation? Learn the key difference between sigma (σ) and standard deviation (SD) and how each measures data variability in statistics.
What Is the Difference Between Sample Standard Deviation (S) and Population Standard Deviation (σ) in Statistics? Learn the key differences between sample standard deviation (S) and population standard deviation (σ) for accurate statistical analysis.
What Is the Difference Between Sigma (σ) and s in Statistics? Learn the key difference between sigma (σ) as population standard deviation and s as sample standard deviation in statistics.
What Is the Difference Between S and Sigma (σ) in Statistics? Learn the key difference between S (sample standard deviation) and σ (population standard deviation) in statistics, explained simply.
Understanding the New Standard Deviation Symbols in Statistics Learn about the new standard deviation symbols: lowercase sigma (σ) for population and 's' for sample. Explore their significance in statistics.
Understanding Standard Deviation in Statistics: A Comprehensive Guide Explore how standard deviation measures data variation in statistics, including the calculation process and its significance.
How to Write Standard Deviation in Your Reports Effectively Learn how to accurately write standard deviation in your reports with clear examples and concise explanations.
Is Standard Deviation Divided by n or n-1? Understanding the Difference Learn why standard deviation uses n-1 for samples and n for populations to ensure unbiased statistical estimates.