A frequency table of grades has five classes​ (A, B,​ C, D,​ F) with frequencies of 22​, 1414​, 1515​, 77​, and 22     respectively. Using​ percentages, what are the relative frequencies of the five​ classes?
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Part 1
Complete the table.
Grade
Frequency
Relative frequency
A
22
enter your response here​%
B
1414
enter your response here​%
C
1515
enter your response here​%
D
77
enter your response here​%
F
22
enter your response here​%
​(Round to two decimal places as​ needed.)

To find the relative frequency in percentages for each grade class, we need to follow these steps:

1. Calculate the total frequency.
2. Divide the frequency of each class by the total frequency.
3. Convert the resulting ratio to a percentage by multiplying by 100.
4. Round to two decimal places.

### Step 1: Calculate the Total Frequency
\[ \text{Total Frequency} = 22 + 1414 + 1515 + 77 + 22 = 3030 \]

### Step 2: Calculate Relative Frequencies
For each grade:

- **A**:
  \[ \text{Relative Frequency (A)} = \left(\frac{22}{3030}\right) \times 100 = 0.726 \approx 0.73\% \]
- **B**:
  \[ \text{Relative Frequency (B)} = \left(\frac{1414}{3030}\right) \times 100 = 46.67\% \]
- **C**:
  \[ \text{Relative Frequency (C)} = \left(\frac{1515}{3030}\right) \times 100 = 49.92\% \]
- **D**:
  \[ \text{Relative Frequency (D)} = \left(\frac{77}{3030}\right) \times 100 = 2.54\% \]
- **F**:
  \[ \text{Relative Frequency (F)} = \left(\frac{22}{3030}\right) \times 100 = 0.726 \approx 0.73\% \]

### Completed Table
| Grade | Frequency | Relative Frequency (%) |
|-------|-----------|------------------------|
| A     | 22        | 0.73                   |
| B     | 1414      | 46.67                  |
| C     | 1515      | 49.92                  |
| D     | 77        | 2.54                   |
| F     | 22        | 0.73                   |

Would you like more details or have any questions?

Here are five questions you might ask:
1. How do you calculate the total frequency in a frequency table?
2. What is the formula for calculating relative frequency?
3. Why do we convert the relative frequency to a percentage?
4. How do you round numbers to two decimal places?
5. Can you explain how relative frequencies help in data analysis?

**Tip:** Always double-check your total frequency before calculating relative frequencies to avoid errors in your results.

Learn how to calculate relative frequencies using a frequency table of grades A, B, C, D, and F with detailed step-by-step instructions. This problem covers statistical concepts such as relative frequency and percentage calculations. Suitable for high school students.

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