Solutoins:

\(\begin{array}{|c|c|}\hline Class & Frequency(f) \\ (1) & (2) \\ \hline 14-18 & 5 \\ \hline 19-23 & 9 \\ \hline 24-28 & 6 \\ \hline 29-33 & 10 \\ \hline ... & ... \\ \hline & n=30 \\ \hline \end{array}\)

To find Mode Class

Here, maximum frequency is 10.

\(\displaystyle\therefore\text{The mode class is}{28.5}-{33.5}\).

\(\displaystyle\therefore{L}=\text{lower boundary point of made class}={28.5}\)

\(\displaystyle\therefore{f}_{{{1}}}=\text{frequensy of the mode class}={10}\)

\(\displaystyle\therefore{f}_{{{0}}}=\text{frequensy of the preceding class}={6}\)

\(\displaystyle\therefore{f}_{{{2}}}=\text{frequensy of the succedding class}={0}\)

\(\displaystyle\therefore{c}=\text{class length of the mode class}={5}\)

\(\displaystyle{Z}={L}+{\left({\frac{{{f}_{{{1}}}-{f}_{{{0}}}}}{{{2}\cdot{f}_{{{1}}}-{f}_{{{0}}}-{f}_{{{2}}}}}}\right)}\cdot{c}\)

\(\displaystyle={28.5}+{\left({\frac{{{10}-{6}}}{{{2}\cdot{10}-{6}-{0}}}}\right)}\cdot{5}\)

\(\displaystyle={28.5}+{\left({\frac{{{4}}}{{{14}}}}\right)}\cdot{5}\)

\(\displaystyle={28.5}+{1.4286}\)

\(\displaystyle={29.9286}\)