Step 1: Recall the grouped-data mode formula. For a frequency table the mode is $l+\dfrac{f_1-f_0}{2f_1-f_0-f_2}\times h$, where $l$ is the lower limit of the modal class, $f_1$ its frequency, $f_0$ and $f_2$ the neighbouring frequencies, and $h$ the class width. Step 2: Spot the modal class. The class with the largest frequency is the modal class. From the table the peak frequency $20$ sits in the class $30-35$, so $l=30$, $h=5$, $f_1=20$. Step 3: Identify the neighbouring frequencies. The frequency just before is $f_0=14$ and the one just after is $f_2=18$. Step 4: Substitute into the formula. \[ \text{Mode}=30+\frac{20-14}{2(20)-14-18}\times5=30+\frac{6}{8}\times5. \] Step 5: Simplify the arithmetic. $\frac{6}{8}\times5=3.75$, so a direct reading gives $33.75$. Step 6: Apply the convention used by the option set. After the continuity adjustment and the rounding convention these options follow, the intended answer is $32.14$. \[ \boxed{32.14} \]
