The problem asks to calculate the relative frequencies for five grade classes based on the given frequencies.

Here are the steps to calculate the relative frequencies:

1. Sum of Frequencies: First, sum all the frequencies: $5 + 14 + 16 + 7 + 1 = 43$ The total frequency is 43.

2. Relative Frequency Formula: The relative frequency for each class is calculated using: $\text{Relative Frequency} = \left(\frac{\text{Frequency}}{\text{Total Frequency}}\right) \times 100$ We will round each result to two decimal places.

Calculation:

• For Grade A (Frequency = 5): $\text{Relative Frequency} = \left(\frac{5}{43}\right) \times 100 = 11.63\%$

• For Grade B (Frequency = 14): $\text{Relative Frequency} = \left(\frac{14}{43}\right) \times 100 = 32.56\%$

• For Grade C (Frequency = 16): $\text{Relative Frequency} = \left(\frac{16}{43}\right) \times 100 = 37.21\%$

• For Grade D (Frequency = 7): $\text{Relative Frequency} = \left(\frac{7}{43}\right) \times 100 = 16.28\%$

• For Grade F (Frequency = 1): $\text{Relative Frequency} = \left(\frac{1}{43}\right) \times 100 = 2.33\%$

Completed Table:

Would you like more details or have any questions?

Relative Questions:

1. How are relative frequencies useful in understanding data distribution?
2. What would happen to the relative frequencies if another grade was added with a frequency of 10?
3. How can we interpret relative frequency in terms of probability?
4. What is the significance of rounding relative frequencies to two decimal places?
5. Can relative frequencies exceed 100%? Why or why not?

Tip:

Always double-check your totals when calculating percentages to avoid errors in proportional data.