Standard Deviation Calculator
Calculate mean, variance, and standard deviation of data.
기본 통계
분산 및 표준편차
Overview
The Standard Deviation Calculator computes the mean, variance, and standard deviation of a data set. It supports both population and sample standard deviation, helping you understand how spread out your data is.
Formula
Mean (μ or x̄) = Σxᵢ / n Population variance (σ²) = Σ(xᵢ - μ)² / N Population std dev (σ) = √(Σ(xᵢ - μ)² / N) Sample variance (s²) = Σ(xᵢ - x̄)² / (n - 1) Sample std dev (s) = √(Σ(xᵢ - x̄)² / (n - 1))
How to Use
- 1Enter data values separated by commas or spaces.
- 2Select whether the data is a population or a sample.
- 3The mean, variance, and standard deviation are calculated automatically.
Tips
- ✔Sample standard deviation divides by n-1 to correct bias (Bessel's correction).
- ✔A smaller standard deviation means data points are closer to the mean.
- ✔In a normal distribution, about 68% of data falls within ±1σ and 95% within ±2σ of the mean.
FAQ
Q. What is the difference between population and sample standard deviation?
Population standard deviation divides by N (total population size), while sample standard deviation divides by n-1 (sample size minus one). The n-1 denominator corrects for bias when estimating from a sample (Bessel's correction).
Q. What is the relationship between variance and standard deviation?
Standard deviation is the positive square root of the variance. Variance is in squared units of the original data, while standard deviation shares the same units as the data, making it more intuitive to interpret.
Q. Where is standard deviation used?
It is used in quality control (Six Sigma), financial risk/volatility measurement, test score analysis, scientific precision evaluation, and any field where understanding data dispersion matters.
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