Standard Deviation Calculator
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How Standard Deviation is Calculated
Example
Dataset: 2, 4, 4, 4, 5, 5, 7, 9
- Count: 8 Mean: 5
- Variance (pop.): 4.0
- Std Dev σ (pop.): 2.0
- Std Dev s (sample): 2.14
Frequently Asked Questions
What is standard deviation?
Standard deviation measures how spread out numbers are from the mean (average). A low standard deviation means the values are clustered close to the mean; a high standard deviation means they are spread over a wider range. It is the square root of variance.
When should I use population vs. sample standard deviation?
Use population standard deviation (σ, divides by N) when you have data for every member of a group. Use sample standard deviation (s, divides by N-1) when your data is a sample drawn from a larger population — which is most real-world scenarios. The N-1 denominator (Bessel's correction) corrects for the bias in estimating population variance from a sample.
What is a "normal" standard deviation?
There is no universal benchmark — standard deviation is meaningful relative to the mean and the context. A test with a mean of 75 and SD of 5 indicates most scores fell between 70–80. One with SD of 20 shows much more variability. The coefficient of variation (SD/mean × 100%) is useful for comparing variability across different scales.
What is the empirical rule (68-95-99.7)?
For normally distributed data: approximately 68% of values fall within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3. This rule is useful for quickly assessing whether a value is typical or an outlier.