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.
Why is SD preferred over Variance?
SD is expressed in the same units as the original data (e.g., dollars, inches), whereas Variance is in squared units, making SD easier to interpret.
What is a "Z-Score"?
A Z-score tells you how many standard deviations a specific data point is from the mean. Z = (X - Mean) / SD.
How is SD used in finance?
It measures volatility (risk). An investment with a high standard deviation has returns that vary widely from the average, implying higher risk.
What is the difference between population and sample standard deviation?
Population standard deviation divides by N (total count), while sample standard deviation divides by N-1 (Bessel's correction) to produce an unbiased estimate. Use population SD when you have data for every member of the group and sample SD when working with a subset. The difference matters most for small samples.