Standard Deviation Calculator
Understanding Standard Deviation
Standard deviation measures the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.
Population Standard Deviation (\(\sigma\))
Use this when your data represents the entire population of interest.
\[ \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}} \]
Sample Standard Deviation (s)
Use this when your data is a sample of a larger population. The denominator is `n-1` to provide an unbiased estimate of the population variance.
\[ s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}} \]
Enter numbers separated by commas, spaces, or new lines.
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