To determine the mean diameter to the appropriate number of significant figures, we follow these steps:

1. Calculate the arithmetic mean: Sum of values = $3.33 + 3.32 + 3.34 + 3.33 + 3.32 = 16.64$ cm. Mean = $\frac{16.64}{5} = 3.328$ cm.

2. Apply Significant Figure Rules: When finding the average of a set of measured values, the result should be reported to the same level of precision (decimal places) as the individual measurements to maintain consistency with the precision of the measuring instrument . Since the original measurements are recorded to two decimal places, the mean must also be rounded to two decimal places.

3. Rounding: In the value 3.328, the digit to be dropped is 8. Since 8 is greater than 5, the preceding digit (2) is increased by one . Thus, the mean diameter is 3.33 cm.