To create a frequency distribution table, you need a data set to work with. Here’s how you would construct one:

1. **Organize the data set**: Gather all the data points you want to categorize. 
2. **Define class intervals**: Divide the range of data into equal intervals.
3. **Tally the frequencies**: Count how many data points fall within each class interval.
4. **Complete the table**: Summarize the intervals and frequencies in a table format.

Let's walk through an example. Suppose we have the following data set representing test scores out of 100:

**Data set**:  
45, 56, 67, 34, 78, 88, 90, 45, 56, 67, 45, 67, 34, 23, 89

### Step 1: Organize the data
This is already provided.

### Step 2: Define Class Intervals
We can define intervals of 10 points, starting from 20 to 30, 30 to 40, and so on.

### Step 3: Tally the Frequencies

| Class Interval | Frequency |
|----------------|-----------|
| 20 - 29        | 1         |
| 30 - 39        | 2         |
| 40 - 49        | 3         |
| 50 - 59        | 2         |
| 60 - 69        | 3         |
| 70 - 79        | 1         |
| 80 - 89        | 2         |
| 90 - 99        | 1         |

### Step 4: Complete the Table
Here’s the final frequency distribution table based on the data.

| **Score Range** | **Frequency** |
|-----------------|---------------|
| 20 - 29         | 1             |
| 30 - 39         | 2             |
| 40 - 49         | 3             |
| 50 - 59         | 2             |
| 60 - 69         | 3             |
| 70 - 79         | 1             |
| 80 - 89         | 2             |
| 90 - 99         | 1             |

This table summarizes how many scores fall within each range of test scores.

Do you want details on any part of the process or have further questions?

Here are five related questions to think about:

1. How would you calculate the relative frequency for each class interval?
2. What is the cumulative frequency, and how can it be added to the table?
3. How would you handle data sets with decimal values in a frequency distribution?
4. How do you choose appropriate class intervals for different data sets?
5. What would a histogram look like for this data set?

**Tip**: When choosing class intervals, ensure that the intervals are of equal size and cover the entire range of your data.

Learn how to make a frequency distribution table for a data set of test scores, including steps like organizing the data, defining class intervals, and tallying frequencies. This example uses test scores: 45, 56, 67, 34, 78, 88, and more. Suitable for students in Grades 6-8.

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