https://file.aiquickdraw.com/mathbot/file/17273384916629iuyocz6.jpg

To determine the number of classes, class intervals, and create a frequency table based on the data provided, we will follow these steps:

1. **Organize the data**: List all the values.
2. **Determine the range**: The range is the difference between the highest and lowest value.
3. **Choose the number of classes**: This can be done using Sturges' Rule \(k = 1 + 3.322 \log N\), where \(N\) is the number of data points (34 in this case).
4. **Calculate the class width**: The class width is determined by dividing the range by the number of classes.
5. **Create the frequency distribution**: Tally the data within each class.

Let's begin by listing and analyzing the data from the image:

**Data**:
\[
\{71, 75, 57, 88, 64, 80, 75, 82, 90, 68, 90, 88, 71, 75, 71, 81, 81, 48, 82, 72, 62, 68, 74, 79, 84, 75, 57, 75, 75, 68, 68, 68, 75, 80\}
\]

### Step 1: Determine the Range
- **Minimum value**: 48
- **Maximum value**: 90
- **Range** = \( 90 - 48 = 42 \)

### Step 2: Determine the Number of Classes
Using Sturges' Rule:
\[
k = 1 + 3.322 \log N = 1 + 3.322 \log 34 \approx 1 + 3.322 \times 1.531 = 6.09 \approx 6
\]
Thus, the number of classes is approximately 6.

### Step 3: Determine the Class Width
\[
\text{Class width} = \frac{\text{Range}}{\text{Number of classes}} = \frac{42}{6} = 7
\]
So, each class will have a width of 7 points.

### Step 4: Create the Class Intervals
The first class will start at the minimum value (48), and each subsequent class will increase by the class width (7).

1. \(48 - 54\)
2. \(55 - 61\)
3. \(62 - 68\)
4. \(69 - 75\)
5. \(76 - 82\)
6. \(83 - 90\)

### Step 5: Frequency Distribution Table

| Class Interval | Frequency |
|----------------|-----------|
| 48 - 54        | 3         |
| 55 - 61        | 2         |
| 62 - 68        | 9         |
| 69 - 75        | 12        |
| 76 - 82        | 6         |
| 83 - 90        | 2         |

Thus, the class intervals and frequencies have been determined.

---

Would you like more details on any of these steps or calculations? Feel free to ask!

### Related Questions:
1. How is Sturges' Rule used in determining the number of classes?
2. Why is it important to choose an appropriate class width?
3. Can we use a different method to determine the number of classes?
4. What are the other methods for constructing frequency tables?
5. How does the range affect the number of classes?

**Tip**: Always round up the number of classes when applying Sturges' Rule to avoid under-representation of data in classes.

Tentukan banyaknya kelas, interval dan buatkan tabel frekuensinya untuk nilai ujian dari 34 mahasiswa.

Learn how to calculate the number of classes, class intervals, and frequency table for a set of 34 student test scores. Using Sturges' Rule and class width calculations, this problem demonstrates key concepts in statistics. Perfect for college-level quantitative methods courses.

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