Standard Deviation Calculator
Population & sample σ, instantly · 표준편차 계산기
Paste a data set to get the count, sum, mean, variance, and both population and sample standard deviation — then drill the concept in the live tool.
How to use this calculator
- Type or paste your numbers, separated by commas, spaces, or new lines.
- Press Calculate (or Ctrl/Cmd + Enter) to see every statistic at once.
- Read both rows: population SD (σ, divide by n) when your data is the whole group, and sample SD (s, divide by n − 1) when it is a sample of a larger population.
숫자를 쉼표·공백·줄바꿈으로 구분해 입력하고 Calculate(또는 Ctrl/Cmd+Enter)를 누르면 개수·합·평균·분산과 모집단(σ, ÷n)·표본(s, ÷n−1) 표준편차가 한 번에 나옵니다.
Population vs sample standard deviation
Standard deviation measures how far values sit from the mean, in the data's own units. The population standard deviation divides the summed squared deviations by n; the sample standard deviation divides by n − 1 (Bessel's correction) so it is an unbiased estimate of a larger population's spread. This calculator shows both — pick the one that matches your data. For the full derivation and the 68-95-99.7 rule, see the standard deviation guide, or review variance and the mean.
표준편차는 값들이 평균에서 떨어진 정도를 데이터의 단위로 나타냅니다. 모집단은 ÷n, 표본은 ÷(n−1)(베셀 보정)으로 나눠 더 큰 모집단의 산포를 불편추정합니다. 자세한 유도는 표준편차 문서를 참고하세요.
Worked example
For the data set 2, 4, 4, 4, 5, 5, 7, 9 (n = 8): the mean is 40 / 8 = 5; the squared deviations sum to 32, so the population variance is 32 / 8 = 4 and the population SD is √4 = 2. The sample variance is 32 / 7 ≈ 4.57, giving a sample SD of ≈ 2.14. Press Try an example above to load this set.
2, 4, 4, 4, 5, 5, 7, 9 (n=8): 평균 5, 제곱편차 합 32 → 모분산 4, 모표준편차 2, 표본분산 32/7 ≈ 4.57, 표본표준편차 ≈ 2.14. 위 "Try an example"로 불러올 수 있습니다.
Frequently asked questions
Which standard deviation should I use? Use the population SD (σ) when your numbers are the entire group you care about; use the sample SD (s) when they are a sample drawn from a larger population you want to estimate.
Why does the sample version divide by n − 1? Dividing by n − 1 (Bessel's correction) offsets the bias from using the sample mean instead of the true mean, making s² an unbiased estimator of the population variance.
What is the difference between variance and standard deviation? Variance is the average squared deviation; the standard deviation is its square root, back in the original units, so it is easier to interpret.
모집단 전체면 σ, 더 큰 모집단의 표본이면 s를 씁니다. 표본은 n−1로 나눠(베셀 보정) 불편추정량이 됩니다. 분산은 제곱편차의 평균, 표준편차는 그 제곱근으로 원래 단위로 돌아온 값입니다.
Keep practicing
Ready to master it? Drill standard deviation and the rest of statistics on C:Stat, read the full concept guide, or browse more tools on the calculators hub.