Variance Variance measures the spread or dispersion of a set of data points around their mean (avera

Question

Variance Variance measures the spread or dispersion of a set of data points around their mean (average). For a group of discrete data, the variance ($\sigma^2$) is calculated as the average of the squared differences between each data point and the mean. $$\sigma^2 = \frac{\sum(x - \bar{x})^2}{n}$$ Standard Deviation The standard deviation is the square root of the variance. It gives a measure of the root-mean-square deviation from the mean, expressed in the same units as the data. $$\sigma = \sqrt{\frac{\sum(x - \bar{x})^2}{n}}$$ Show in an algebraic way that, an alternative expression for standard deviation of a set of discrete data is given by $\sigma = \sqrt{\frac{\sum x^2}{n} - \bar{x}^2}$.

Accepted Answer

$\sigma=\sqrt{\frac{\sum x^2}{n}-\bar{x}^2}$ (shown)

Variance and Standard Deviation

Variance and Standard Deviation

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