To calculate the relative frequencies as percentages, we first find the total number of grades by summing the frequencies. Then, for each class, we divide the frequency by the total and multiply by 100 to convert to a percentage.

Step-by-Step Solution

1. Calculate the Total Frequency: $2 + 12 + 16 + 8 + 2 = 40$

2. Calculate the Relative Frequencies for Each Grade (in percentages):

   • For A: $\frac{2}{40} \times 100 = 5\%$
   • For B: $\frac{12}{40} \times 100 = 30\%$
   • For C: $\frac{16}{40} \times 100 = 40\%$
   • For D: $\frac{8}{40} \times 100 = 20\%$
   • For F: $\frac{2}{40} \times 100 = 5\%$

Summary of Relative Frequencies

Grade	Frequency	Relative Frequency (%)
A	2	5%
B	12	30%
C	16	40%
D	8	20%
F	2	5%

Would you like further details on how to interpret this table?

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Related Questions

1. How would relative frequencies change if the total number of grades increased or decreased?
2. What are cumulative frequencies, and how would they apply here?
3. Can you create a histogram based on this data?
4. How do relative frequencies help in understanding the distribution of grades?
5. What if there were more categories, like "Pass" and "Fail"—how would that change the analysis?

Tip

Relative frequencies are useful for comparing data in percentages, making it easier to understand proportions and distributions across different sample sizes.