A professor records the following final grades in one course. Construct a frequency table for the grades.

A

A

A

Upper BB

Upper BB

B

B

B

B

B

B

C

C

C

C

C

C

C

Upper CC

Upper DD

D

D

Upper DD

Upper FF

Question content area bottom

Part 1

Complete the table.

​(Type an integer or decimal rounded to the nearest tenth as​ needed.)

Part 2

Part 3

Grade

Frequency

Relative frequency

Cumulative frequency

A

33

12.512.5​%

33

B

88

33.333.3​%

1111

C

enter your response here

enter your response here​%

enter your response here

To solve this problem, we'll start by organizing the grades in a **frequency table** and then compute the **relative frequency** and **cumulative frequency**.

### Step 1: Frequency Count

Here’s the list of grades provided:

- **A**: 3 occurrences
- **B**: 8 occurrences
- **C**: 9 occurrences
- **D**: 4 occurrences
- **F**: 1 occurrence

### Step 2: Total Number of Grades

Adding up all the occurrences, we get:
\[
3 + 8 + 9 + 4 + 1 = 25
\]

So, the total number of grades is **25**.

### Step 3: Calculating Relative Frequency

The **relative frequency** for each grade is calculated as:
\[
\text{Relative Frequency} = \frac{\text{Frequency}}{\text{Total Number of Grades}} \times 100
\]

We'll round each relative frequency to the nearest tenth as needed.

### Step 4: Calculating Cumulative Frequency

The **cumulative frequency** is the running total of frequencies, starting from the top of the table.

Now, let's construct the full table:

| Grade | Frequency | Relative Frequency (%) | Cumulative Frequency |
|-------|-----------|------------------------|----------------------|
| A     | 3         | \( \frac{3}{25} \times 100 = 12.0\% \) | 3                    |
| B     | 8         | \( \frac{8}{25} \times 100 = 32.0\% \) | 3 + 8 = 11           |
| C     | 9         | \( \frac{9}{25} \times 100 = 36.0\% \) | 11 + 9 = 20          |
| D     | 4         | \( \frac{4}{25} \times 100 = 16.0\% \) | 20 + 4 = 24          |
| F     | 1         | \( \frac{1}{25} \times 100 = 4.0\% \)  | 24 + 1 = 25          |

### Completed Table

| Grade | Frequency | Relative Frequency (%) | Cumulative Frequency |
|-------|-----------|------------------------|----------------------|
| A     | 3         | 12.0%                  | 3                    |
| B     | 8         | 32.0%                  | 11                   |
| C     | 9         | 36.0%                  | 20                   |
| D     | 4         | 16.0%                  | 24                   |
| F     | 1         | 4.0%                   | 25                   |

### Final Answer for Part 2
The row for grade **C**:
- **Frequency**: 9
- **Relative Frequency**: 36.0%
- **Cumulative Frequency**: 20

Would you like further clarification on these calculations?

---

#### 5 Practice Questions
1. How do you calculate the cumulative frequency in a frequency table?
2. What is the purpose of relative frequency in a dataset?
3. How would the table change if there were an additional "A" grade?
4. Why might a professor use a frequency table to analyze student grades?
5. How can you interpret the cumulative frequency of each grade?

#### Quick Tip
Remember that cumulative frequency is simply the running total of occurrences, helping to show the buildup across different categories or groups.

A professor records the following final grades in one course. Construct a frequency table for the grades.

A

A

A

Upper BB

Upper BB

B

B

B

B

B

B

C

C

C

C

C

C

C

Upper CC

Upper DD

D

D

Upper DD

Upper FF

Question content area bottom

Part 1

Complete the table.

​(Type an integer or decimal rounded to the nearest tenth as​ needed.)

Part 2

Part 3

Grade

Frequency

Relative frequency

Cumulative frequency

A

33

12.512.5​%

33

B

88

33.333.3​%

1111

C

enter your response here

enter your response here​%

enter your response here

Construct a frequency table for student grades in a college course, including frequency, relative frequency, and cumulative frequency. Learn to calculate and interpret each type of frequency with real-world examples.

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