https://file.aiquickdraw.com/mathbot/file/1726436660160k3sddkf4.jpg

The image contains a set of numbers followed by a few tasks to perform, including:

1. Find the **midpoints**.
2. Find the **relative frequency** in percentage.
3. Determine the **cumulative frequency** (ascending and descending).
4. Calculate the **number of classes**, which is given as **7**.

### Step 1: Organizing the Data

First, let's list out the values provided:
- 66, 65, 73, 74, 85, 91, 77, 30, 32, 45, 69, 57, 52, 63, 40, 66, 30, 92, 70, 64

### Step 2: Creating Classes
The number of classes is given as 7. To determine the class width, we first calculate the range.

1. **Range = Maximum value - Minimum value**
   - Maximum = 92
   - Minimum = 30
   - Range = 92 - 30 = 62

2. **Class width** = (Range) / (Number of classes)
   - Class width = \( \frac{62}{7} \approx 8.86 \), we will round this to 9.

So, the class intervals will each span a width of 9.

### Step 3: Forming Class Intervals

The first class can start from the minimum value (30), and the width will be 9. The intervals will be:
- 30–38
- 39–47
- 48–56
- 57–65
- 66–74
- 75–83
- 84–92

Now we can organize the values into these intervals.

Let me calculate the midpoints, relative frequencies, and cumulative frequencies.Here are the results based on the given dataHere are the results based on the given 

### 1. Class Intervals and Midpoints:
| Class Interval | Midpoint |
| -------------- | -------- |
| 30–38          | 34.0     |
| 39–47          | 43.0     |
| 48–56          | 52.0     |
| 57–65          | 61.0     |
| 66–74          | 70.0     |
| 75–83          | 79.0     |
| 84–92          | 88.0     |

### 2. Frequency Distribution:
| Class Interval | Frequency |
| -------------- | --------- |
| 30–38          | 3         |
| 39–47          | 2         |
| 48–56          | 1         |
| 57–65          | 4         |
| 66–74          | 6         |
| 75–83          | 1         |
| 84–92          | 3         |

### 3. Relative Frequency (%):
| Class Interval | Relative Frequency (%) |
| -------------- | ---------------------- |
| 30–38          | 15.0                   |
| 39–47          | 10.0                   |
| 48–56          | 5.0                    |
| 57–65          | 20.0                   |
| 66–74          | 30.0                   |
| 75–83          | 5.0                    |
| 84–92          | 15.0                   |

### 4. Cumulative Frequency:
- **Ascending**: [3, 5, 6, 10, 16, 17, 20]
- **Descending**: [20, 17, 15, 14, 10, 4, 3]

Would you like more details on any of these calculations?

### Related Questions:
1. How is the class width chosen for creating intervals?
2. What does the midpoint of a class interval represent?
3. How is the relative frequency calculated in a frequency distribution?
4. What is the significance of cumulative frequency in data analysis?
5. Can the number of classes be adjusted, and how does that affect the results?

### Tip:
Always ensure the class intervals do not overlap and completely cover the range of your data for accurate frequency distribution.

Find midpoints, relative frequency, cumulative frequency, and determine the number of classes for the given data set.

Learn how to calculate midpoints, relative frequency, and cumulative frequency for a given data set. The solution includes the use of class intervals, class width calculation, and determining the relative frequency and cumulative frequency.

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