标准差计算器

Use this free standard deviation calculator to calculate sample and population standard deviation from a data set.
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样本标准差与总体标准差

样本标准差

当您的数据是较大总体的样本时使用。除以 n-1（贝塞尔校正）以提供无偏估计。

s = √[Σ(xᵢ - x̄)² / (n - 1)]

总体标准差

当您的数据代表整个总体时使用。除以 N。

σ = √[Σ(xᵢ - μ)² / N]

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How our standard deviation calculator works

1

Enter your data set

Type your numbers separated by commas or newlines. The calculator accepts any size data set from a few points to thousands.

2

Choose sample or population

Select Sample (when your data is a subset of a larger population) or Population (when you have all values). The formulas differ slightly.

3

See the full statistics

Get the mean, variance, standard deviation, range, and a histogram. Standard deviation tells you the typical spread of values from the mean.

Key things to know about our standard deviation calculator:

  • 68-95-99.7 rule: For a normal distribution, 68% of values fall within 1 SD of the mean, 95% within 2 SD, and 99.7% within 3 SD. Useful for quality control and grading curves.
  • Sample vs population: Use Sample (divide by n-1) when generalizing to a larger population. Use Population (divide by n) when you have all values.
  • Use cases: Investment volatility, test score spread, manufacturing tolerances, scientific data analysis, and grade normalization are common uses.

For related calculations, try our percentage calculator.