Question

For a frequency distribution standard deviation is computed by applying the formula
(a) $\mathrm{\sigma }=\sqrt{\frac{\mathrm{\Sigma }f{d}^2}{\mathrm{\Sigma }f}-{\left(\frac{\mathrm{\Sigma }fd}{\mathrm{\Sigma }f}\right)}^2}$

(b) $\mathrm{\sigma }=\sqrt{{\left(\frac{\mathrm{\Sigma }fd}{\mathrm{\Sigma }f}\right)}^2-\frac{\mathrm{\Sigma }f{d}^2}{\mathrm{\Sigma }f}}$

(c) $\mathrm{\sigma }=\sqrt{\frac{\mathrm{\Sigma }f{d}^2}{\mathrm{\Sigma }f}-\frac{\mathrm{\Sigma }fd}{\mathrm{\Sigma }f}}$

(d) $\sqrt{{\left(\frac{\mathrm{\Sigma }fd}{\mathrm{\Sigma }f}\right)}^2-\frac{\mathrm{\Sigma }f{d}^2}{\mathrm{\Sigma }f}}$

Answer 1

$\left(\mathrm{a}\right)\sigma =\sqrt{\frac{{\sum }_{}^{}f{d}^2}{{\sum }_{}^{}f}-{\left(\frac{{\sum }_{}^{}fd}{{\sum }_{}^{}f}\right)}^2}$