The bvariance/b ((\sigma2)) is a measure of spread of a data set, and indicates how much each data point deviates from the mean.
(\sigma2 = \dfrac{\sum{(x-\bar{x})^2}}{n} = \dfrac{\sum{x^2}}{n} - \Big(\dfrac{\sum{x}}{n}\Big)^2)
Alternatively, using the bsummary statistic/b (S):
(S = \sum{(x-\bar{x})^2} = \sum{x^2} - \dfrac{(\sum{x})^2}{n})
(\sigma2 = \dfrac{S_}{n})
The bstandard deviation/b ((\sigma)) is the square root of the variance.
(\sigma = \sqrt{\dfrac{\sum{(x-\bar{x})2}}{n}} = \sqrt{\dfrac{\sum{x^2}}{n} - \Big(\dfrac{\sum{x}}{n}\Big)^2})
Alternatively:
(\sigma = \sqrt{\dfrac{S}{n}})
[b]uGrouped frequency[/u]/b
(\sigma2 = \dfrac{\sum{f(x-\bar{x})^2}}{\sum{f}} = \dfrac{\sum{fx^2}}{\sum{f}} - \Big(\dfrac{\sum{fx}}{\sum{f}}\Big)^2)
(\sigma = \sqrt{\dfrac{\sum{f(x-\bar{x})2}}{\sum{f}}} = \sqrt{\dfrac{\sum{fx^2}}{\sum{f}} - \Big(\dfrac{\sum{fx}}{\sum{f}}\Big)^2})
[b]uVariance[/u]/b
(\sigma2 = \dfrac{\sum{(x-\bar{x})^2}}{n} = \dfrac{\sum{x^2}}{n} - \Big(\dfrac{\sum{x}}{n}\Big)^2)
For grouped frequency:
(\sigma2 = \dfrac{\sum{f(x-\bar{x})^2}}{\sum{f}} = \dfrac{\sum{fx^2}}{\sum{f}} - \Big(\dfrac{\sum{fx}}{\sum{f}}\Big)^2)
[b]uStandard deviation[/u]/b
(\sigma = \sqrt{\dfrac{\sum{(x-\bar{x})2}}{n}} = \sqrt{\dfrac{\sum{x^2}}{n} - \Big(\dfrac{\sum{x}}{n}\Big)^2})
For grouped frequency:
(\sigma = \sqrt{\dfrac{\sum{f(x-\bar{x})2}}{\sum{f}}} = \sqrt{\dfrac{\sum{fx^2}}{\sum{f}} - \Big(\dfrac{\sum{fx}}{\sum{f}}\Big)^2})