For a frequency distribution standard deviation is computed by applying the formula
(a) $σ = \sqrt{\frac{Σ f d^{2}}{Σ f} - {(\frac{Σ f d}{Σ f})}^{2}}$

(b) $σ = \sqrt{{(\frac{Σ f d}{Σ f})}^{2} - \frac{Σ f d^{2}}{Σ f}}$

(c) $σ = \sqrt{\frac{Σ f d^{2}}{Σ f} - \frac{Σ f d}{Σ f}}$

(d) $\sqrt{{(\frac{Σ f d}{Σ f})}^{2} - \frac{Σ f d^{2}}{Σ f}}$

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Solution

$(a) σ = \sqrt{\frac{\sum_{}^{} f d^{2}}{\sum_{}^{} f} - {(\frac{\sum_{}^{} f d}{\sum_{}^{} f})}^{2}}$

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