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Variance and Standard Deviation - Standard Deviation of a Continuous Frequency Distribution

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notes

The given continuous frequency distribution can be represented as a discrete frequency distribution by replacing each class by its mid-point.
If there is a frequency distribution of n classes each class defined by its mid-point `x_i` with frequency` f_i`, the standard deviation will be obtained by the formula

σ = \[\sqrt{{\frac{1}{N}}\displaystyle\sum_{i=1}^{n} f_i (x_i - \bar{x} )^2} \] 
where `bar x` is the mean of the distribution and
N =  \[\displaystyle\sum_{i=1}^{n} f_i \].

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