Explanation

(c)
[table] Class | $\mathbf{f}_{\mathbf{i}}$ | $\mathbf{y}_{\mathbf{i}}$ | $\mathbf{D}_{\mathbf{i}}\mathbf{=}\mathbf{y}_{\mathbf{i}}\mathbf{- A\ }$
$\mathbf{A = 25}$ | $\mathbf{f}_{\mathbf{i}}\mathbf{d}_{\mathbf{i}}$ | $\mathbf{f}_{\mathbf{i}}\mathbf{d}_{\mathbf{i}}^{\mathbf{2}}$ ; 0-10 | 1 | 5 | -20 | -20 | 400 ; 10-20 | 3 | 15 | -10 | -30 | 300 ; 20-30 | 4 | 25 | 0 | 0 | 0 ; 30-40 | 2 | 35 | 10 | 20 | 200 ; Total | 10 | | | -30 | 900 [/table]
$\therefore\ \ \sigma^{2} = \frac{\Sigma f_{i}d_{i}^{2}}{\Sigma f_{i}} - \left( \frac{\Sigma f_{i}d_{i}^{\ }}{\Sigma f_{i}} \right)^{2}$
$= \frac{900}{10} - \left( \frac{- 30}{10} \right)^{2} = 90 - 9$
$\Rightarrow \ \ \ \sigma^{2} = 81$
$\Rightarrow \sigma = 9$