Free Standard Deviation Calculator — Variance & Stats | NovaCalculator
Calculate population or sample standard deviation, variance, and mean. Shows all statistical calculations step-by-step.
Formula
σ = √(Σ(x - μ)² / N)
Standard deviation is the square root of the variance, representing the average distance from the mean.
Worked Examples
Example 1: Test Scores
Problem:Scores: 80, 85, 90
Solution:Mean = 85. Variance = ((5² + 0² + 5²)/3) = 50/3 = 16.67. SD = √16.67 ≈ 4.08.
Result:Mean: 85, SD: 4.08
Frequently Asked Questions
What is Standard Deviation?
It is a statistic that measures the dispersion of a dataset relative to its mean. A low SD indicates data points tend to be close to the mean; a high SD indicates high variation.
What is Variance?
Variance is the average of the squared differences from the mean. Standard Deviation is simply the square root of Variance.
Can Standard Deviation be negative?
No. Since it involves squaring differences and then taking a square root, it must always be non-negative. It can be 0 if all data points are identical.
What affects Standard Deviation the most?
Outliers (extreme values) can heavily influence the SD because their distance from the mean is squared, disproportionately increasing the result.