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Fundamentals

Sample vs Population Standard Deviation: Which One Do You Need?

The difference between dividing by n and dividing by n − 1 what Bessel's correction actually does, and how to pick the right formula for your data.

RSDCalc Team · 1 min read
On this page
  1. Population standard deviation
  2. Sample standard deviation
  3. A rule of thumb
  4. Related reading

It’s the question every stats student trips over: do you divide by n or by n − 1 when computing the standard deviation? The short answer:

  • Population: divide by n
  • Sample: divide by n − 1

But what does that mean? See the side-by-side formulas in our Standard Deviation Formulas section on the home page.

Population standard deviation

You use the population formula when your data covers every member of the group you care about. Every employee in your company. Every student in your class. Every transaction last quarter.

σ = √( Σ(xᵢ − μ)² / n )

Because there’s no “outside” to your data, the mean you computed is the true arithmetic mean, and dividing by n gives you the true standard deviation.

Sample standard deviation

You use the sample formula when your data is a subset drawn from a larger population. A random sample of 200 employees from the entire workforce. Lab measurements from a few replicate trials of a much larger experimental space.

s = √( Σ(xᵢ − x̄)² / (n − 1) )

Why n − 1? Because the mean you computed (the sample mean) is itself an estimate. Dividing by n would systematically underestimate the true population standard deviation. Subtracting 1 from the denominator Bessel’s correction corrects that bias. The NIST/SEMATECH e-Handbook of Statistical Methods covers the formal derivation.

A rule of thumb

If you’re describing the data you have in front of you and that’s the whole story → population. If you’re trying to infer something about a larger group from a smaller one → sample.

Sample is the more common choice in practice, which is why the RSD Calculator defaults to it.

Calculators and spreadsheets label the two differently. On most scientific calculators the sample value is sx or Sx and the population value is σx, as shown in How to Calculate RSD on a Scientific Calculator. In Excel they are STDEV.S and STDEV.P, covered in Relative Standard Deviation in Excel.

Fundamentals ← All guides

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Enter your measurements in the RSD Calculator to confirm the mean, standard deviation and %RSD, with sample or population SD.

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