By taking classes 30 - 40, 40 - 50, 50 - 60,.. ., construct a frequency table for the following data:
` " 65 34 74 49 52 35" `
` " 71 55 61 40 56 38 " `
` " 52 56 52 33 60 35 " `
` " 49 37 53 50 44 30" `
`" 62 50 47 45 47 50 " `
` " 63 61 54 58 47 64 " `
` " 37 38 44 42 47 55 " `
` " 70 33 75 49 47 30" `
` " 60 69" `

Answer

To construct a frequency table based on the given data, we will follow these steps:

### Step 1: Identify the Class Intervals
The class intervals are given as:
- 30 - 40
- 40 - 50
- 50 - 60
- 60 - 70
- 70 - 80

### Step 2: List the Data
The provided data is:
```
65, 34, 74, 49, 52, 35,
71, 55, 61, 40, 56, 38,
52, 56, 52, 33, 60, 35,
49, 37, 53, 50, 44, 30,
62, 50, 47, 45, 47, 50,
63, 61, 54, 58, 47, 64,
37, 38, 44, 42, 47, 55,
70, 33, 75, 49, 47, 30,
60, 69
```

### Step 3: Count Frequencies for Each Class Interval
Now we will count how many numbers fall into each class interval:

- **30 - 40**:
- Numbers: 34, 35, 38, 33, 30, 37, 39
- Frequency: 7

- **40 - 50**:
- Numbers: 49, 40, 44, 47, 45, 47, 49
- Frequency: 7

- **50 - 60**:
- Numbers: 52, 55, 56, 52, 56, 52, 53, 50, 54, 58
- Frequency: 10

- **60 - 70**:
- Numbers: 65, 61, 62, 63, 61, 64, 60, 69
- Frequency: 8

- **70 - 80**:
- Numbers: 74, 71, 75
- Frequency: 3

### Step 4: Construct the Frequency Table
Now we can organize this information into a frequency table:

| Class Interval | Class Mark | Frequency |
|----------------|------------|-----------|
| 30 - 40 | 35 | 7 |
| 40 - 50 | 45 | 7 |
| 50 - 60 | 55 | 10 |
| 60 - 70 | 65 | 8 |
| 70 - 80 | 75 | 3 |

### Final Frequency Table
The final frequency table summarizes the data as follows:

| Class Interval | Frequency |
|----------------|-----------|
| 30 - 40 | 7 |
| 40 - 50 | 7 |
| 50 - 60 | 10 |
| 60 - 70 | 8 |
| 70 - 80 | 3 |

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