Standard Deviation Calculator
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Guide: Standard Deviation and Variance
Variance measures how spread out data is around the mean. It is calculated as the average of squared deviations from the mean. A larger variance indicates more dispersed data. It is a fundamental measure of dispersion in statistics.
Standard deviation is the square root of the variance. It is expressed in the same units as the original data, making interpretation easier. For example, if average sales are 1000 with a standard deviation of 200, typical values typically fall between 800-1200.
Population vs. sample: Population variance divides by N and applies to the entire population. Sample variance divides by N-1 and is a better estimate for a larger population based on a sample. This is Bessel's correction that biases the estimate.
Interpretation: A small standard deviation means data clusters around the mean. A large one means wide spread of values. The 68-95-99.7 rule states that approximately 68% of data falls within one standard deviation, 95% within two, and 99.7% within three.