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σ

Standard Deviation Calculator

Population/sample stdev, variance, and SEM.

Separate with commas, spaces, or newlines. Sample uses Bessel’s n−1; population divides by n. SEM is always sample stdev ÷ √n.

Stdev s
1.58113883008
Variance s²
2.5
SEM
0.707106781187
Mean
3
Count
5
Min
1
Max
5

Sample: Σ(x−x̄)² / (n−1) · SEM = s / √n

关于Standard Deviation Calculator

Standard deviation and variance measure how spread out numbers are. For a full population, divide the sum of squared deviations by n (σ and σ²). For a sample estimating a population, use Bessel’s correction and divide by n−1 (s and s²). The standard error of the mean (SEM) is the sample standard deviation divided by √n — a gauge of how much the sample mean itself may vary. Paste a comma-, space-, or newline-separated list and switch between sample and population to see stdev, variance, and SEM together, plus mean, count, min, and max. Sample mode needs at least two numbers. Everything runs in your browser; nothing is sent to toco.tools servers.

使用方法

  1. Enter numbers separated by commas, spaces, or newlines
  2. Choose sample (n−1) or population (n)
  3. Read stdev, variance, and SEM

常见问题

What’s the difference between sample and population?

Population divides the sum of squared deviations by n. Sample uses Bessel’s correction (n−1) when estimating a population from a subset. Everyday analysis usually wants the sample formulas.

What is SEM?

The standard error of the mean: sample stdev s divided by √n. It uses that definition on both tabs. It isn’t available with fewer than two numbers.

Is my input sent anywhere?

No. All calculation runs in your browser; nothing is sent to toco.tools servers.