Standard Deviation Calculator
Calculate mean, variance, and standard deviation (population and sample) of a dataset.
Data Input
Mean (Average)--
Population SD (σ)For entire population
--Sample SD (s)For a subset/sample
--Count: 0 numbers processed
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Understanding the Bell Curve
Standard Deviation (SD) in statistics reveals the "story" behind an average. Two classes could both have an average test score of 80%, but one class might have everyone scoring between 75-85 (Low SD), while the other has half the class failing and half getting 100s (High SD).
The 68-95-99.7 Rule
For data that follows a normal distribution (the classic Bell Curve):
- 68% of data falls within 1 SD of the mean.
- 95% of data falls within 2 SDs.
- 99.7% of data falls within 3 SDs.
Population vs. Sample
Population SD (σ): Use this when you have data for every single member of a group.
Sample SD (s): Use this when you only have a subset of data. The formula divides by n-1 (Bessel's Correction) to account for the uncertainty of estimating a whole population from a small sample.