A professor records the following final grades in one course. Construct a frequency table for the grades.
A
A
A
Upper A
Upper B
B
B
B
B
B
B
C
 
C
C
C
C
C
C
Upper C
Upper C
D
D
Upper F
Upper F
Question content area bottom
Part 1
Complete the table.
​(Type an integer or decimal rounded to the nearest tenth as​ needed.)
Part 2Part 3Part 4
Grade
Frequency
Relative frequency
Cumulative frequency
A
  
4
  
16.7​%
  
4
B
  
7
  
29.2​%
  
11
C
  
9
  
37.5​%
  
20
D
  
enter your response here
  
enter your response here​%
  
enter your response here


Let's complete the missing parts of the frequency table step by step, beginning with the given information and continuing through each required calculation.

### Step 1: Calculate the Frequency of Each Grade
From the provided grades, we already have:
- **A**: 4 occurrences
- **B**: 7 occurrences
- **C**: 9 occurrences
- **D**: 2 occurrences (from the grade list: two D's)
- **F**: 2 occurrences (from the grade list: two F's)

### Step 2: Calculate Total Number of Grades
The total number of grades is the sum of the frequencies:
\[
4 \, (\text{A}) + 7 \, (\text{B}) + 9 \, (\text{C}) + 2 \, (\text{D}) + 2 \, (\text{F}) = 24
\]

### Step 3: Calculate the Relative Frequency for Each Grade
The relative frequency is calculated by dividing the frequency of each grade by the total number of grades (24) and multiplying by 100 to convert to a percentage.

- **A**: \(\frac{4}{24} \times 100 = 16.7\%\)
- **B**: \(\frac{7}{24} \times 100 = 29.2\%\)
- **C**: \(\frac{9}{24} \times 100 = 37.5\%\)
- **D**: \(\frac{2}{24} \times 100 = 8.3\%\)
- **F**: \(\frac{2}{24} \times 100 = 8.3\%\)

### Step 4: Calculate the Cumulative Frequency for Each Grade
Cumulative frequency is the running total of frequencies as you move down the table.

- **A**: 4
- **B**: 4 (A) + 7 (B) = 11
- **C**: 11 (A + B) + 9 (C) = 20
- **D**: 20 (A + B + C) + 2 (D) = 22
- **F**: 22 (A + B + C + D) + 2 (F) = 24

### Completed Frequency Table

| Grade | Frequency | Relative Frequency (%) | Cumulative Frequency |
|-------|-----------|------------------------|----------------------|
| A     | 4         | 16.7%                  | 4                    |
| B     | 7         | 29.2%                  | 11                   |
| C     | 9         | 37.5%                  | 20                   |
| D     | 2         | 8.3%                   | 22                   |
| F     | 2         | 8.3%                   | 24                   |

This completes the frequency table. 

Would you like further explanation or clarification?

### Additional Questions:
1. What is the significance of the cumulative frequency in this context?
2. How does relative frequency differ from absolute frequency?
3. How would the table change if there were more grades or categories?
4. What does the distribution of grades tell us about the performance of the class?
5. How would you calculate the mean grade from this frequency table?

### Tip:
Cumulative frequency helps visualize how data accumulates across categories and can be useful for percentile calculations.

A professor records the following final grades in one course. Construct a frequency table for the grades. A, A, A, A, B, B, B, B, B, B, C, C, C, C, C, C, C, C, C, C, D, D, F, F. Complete the table with frequency, relative frequency, and cumulative frequency.

Learn how to construct a frequency table for a course's final grades, including calculations for frequency, relative frequency, and cumulative frequency. This problem covers basic statistical concepts suitable for high school students in Grades 9-12.

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