Standard Deviation Calculator
Enter a list of numbers to calculate the mean, variance, and standard deviation — a measure of how spread out the values are from the average.
Show solution steps
Formula
Population: σ = √( Σ(x−μ)2 / n )
Sample: s = √( Σ(x−x̄)2 / (n−1) )
Use population SD when your numbers are the entire group you care about; use sample SD when your numbers are a sample drawn from a larger population you're trying to estimate.
Worked Example
For the dataset [2, 4, 4, 4, 5, 5, 7, 9]: mean = 5, population standard deviation = 2.
How to Use
- Enter your numbers separated by commas or spaces.
- Choose population or sample standard deviation.
- Read the mean, variance, and standard deviation instantly.
Frequently Asked Questions
Why does sample SD divide by (n-1) instead of n?
This is Bessel's correction u2014 dividing by (n-1) instead of n corrects for the bias that occurs when estimating a population's variance from a smaller sample, giving a less biased estimate.
What does a high standard deviation mean?
It means your data points are, on average, further from the mean u2014 the dataset is more spread out or volatile. A low standard deviation means the values cluster tightly around the mean.
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