Given the frequency distribution: \(\begin{array}{|c|c|} \hline \text{Class Interval} & \text{Frequency} \\ \hline 0-9 & 1 \\ 10-19 & 5 \\ 20-29 & 6 \\ 30-39 & 12 \\ 40-49 & 8 \\ 50-59 & 3 \\ \hline\end{array}\) The modal class is \(30-39\) with frequency \(f_1 = 12\), \(f_0 = 6\) (previous class), \(f_2 = 8\) (next class), and the lower boundary \(L = 29.5\) with class width \(h = 10\). Using the mode formula: \(\text{Mode} = L + \left( \frac{f_1 - f_0}{(f_1 - f_0) + (f_1 - f_2)} \right) \times h\) Substituting the values: \(\text{Mode} = 29.5 + \left( \frac{12 - 6}{(12 - 6) + (12 - 8)} \right) \times 10\) \(\text{Mode} = 29.5 + \left( \frac{6}{6 + 4} \right) \times 10 = 29.5 + \left( \frac{6}{10} \right) \times 10 = 29.5 + 6 = 35.5\)