In statistics, understanding the spread or dispersion of a dataset is just as important as knowing its average. Standard deviation measures the amount of variation or dispersion of a set of values relative to its mean. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. This metric is foundational in finance, quality control, and scientific research for assessing risk and reliability.
Standard Deviation Formulas
Population (σ): √[ Σ(x - μ)² / N ]
Sample (s): √[ Σ(x - x̄)² / (n - 1) ]
How to Use This Calculator
- Enter your numerical dataset, separating each number with a comma or space.
- Select whether your data represents an entire Population or a smaller Sample.
- Click Calculate to instantly view the mean, variance, and standard deviation.
Frequently Asked Questions (FAQ)
Why do we divide by n-1 for a sample?
Dividing by n-1 instead of n applies Bessel's correction. When working with a sample instead of an entire population, dividing by the exact number of observations tends to systematically underestimate the true population variance. Subtracting 1 corrects this bias, providing a more accurate statistical estimate.
What is the difference between variance and standard deviation?
Variance is the average of the squared differences from the Mean. Because it is squared, it is not in the same unit of measurement as the original data. Standard deviation is simply the square root of the variance, returning the dispersion metric back to the original units, making it much easier to interpret.