Standard Deviation Calculator
Standard deviation measures how spread out the numbers in a dataset are from their mean. A low SD means values are clustered near the mean; a high SD means they are widely spread. This calculator gives both sample (n-1) and population SD, along with variance, mean, min and max.
Enter comma-separated numbers, e.g. 10, 20, 30, 40, 50
How it works
The mean is the average. Variance is the average of squared differences from the mean. Standard deviation is the square root of variance. Use sample SD (n-1) when your data is a sample from a larger population; use population SD (n) when you have every data point.
Mean = Σx / n | Sample SD = √(Σ(x - mean)² / (n-1))Example. For the values 4, 8, 15, 16, 23, 42: mean = 18, sample SD ≈ 14.3.
Frequently asked questions
Sample vs population SD - which should I use?
Use sample SD (n-1) when your data is a sample taken from a larger population. Use population SD (n) when you have measured the entire population. In most practical cases, sample SD is correct.
What does a high standard deviation mean?
A high SD means the data points are spread far from the average. Whether that is 'good' or 'bad' depends on context - in finance, high SD means higher volatility; in manufacturing, low SD means better consistency.
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