Statistics

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Standard deviation is the

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1. **Conceptual Definition**: Standard deviation ($\sigma$) measures the amount of variation or dispersion of a set of values relative to their mean.
2. **Mathematical Relation**: It is defined mathematically as the **positive square root of the variance**.
3. **Formula**: $\sigma = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n}}$.
4. **Why Square Root?**: Taking the square root brings the dispersion metric back to the same units as the original data (whereas variance is in units squared).

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