Standard Deviation Calculator
Calculate mean, variance, and standard deviation with step-by-step work.
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Summary Statistics
Count (N)
Sum
Mean (Average)
Range
Minimum
Maximum
Population (divide by N)
Variance (σ²)
Std Dev (σ)
Sample (divide by N-1)
Variance (s²)
Std Dev (s)
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Frequently Asked Questions
What is the difference between population and sample standard deviation? +
Population standard deviation divides by N (the total number of values), while sample standard deviation divides by N-1. Use population when your data includes every member of the group. Use sample when your data is a subset of a larger group.
How is standard deviation calculated? +
First, find the mean (average). Then subtract the mean from each value and square the result. Average those squared differences (divide by N for population, N-1 for sample). Finally, take the square root of that average.
What does a high standard deviation mean? +
A high standard deviation means the data points are spread out over a wide range from the mean. A low standard deviation means the data points tend to be close to the mean. It measures the amount of variation in a data set.
What is variance? +
Variance is the average of the squared differences from the mean. It's the standard deviation squared. While variance gives you the spread of data, standard deviation is more commonly used because it's in the same units as the original data.
Is my data stored anywhere? +
No. All calculations happen entirely in your browser using JavaScript. Your data is never sent to any server or stored anywhere.
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