Following are the marks obtained by 30 students in an examination :
`{:(15,20,8,9,10),(16,17,20,24,30),(44,47,38,36,40),(27,25,28,30,19),(7,11,21,31,41),(37,47,23,20,17):}`
Taking class intervals 0-10 , 10-20,............ ., 40-50, construct a frequency table.

Answer

To construct a frequency table based on the marks obtained by 30 students, we will follow these steps:

### Step 1: Organize the Data
First, we will list out all the marks obtained by the students:
- Marks: 15, 20, 8, 9, 10, 16, 17, 20, 24, 30, 44, 47, 38, 36, 40, 27, 25, 28, 30, 19, 7, 11, 21, 31, 41, 37, 47, 23, 20, 17

### Step 2: Define the Class Intervals
We will define the class intervals as follows:
- 0 - 10
- 10 - 20
- 20 - 30
- 30 - 40
- 40 - 50

### Step 3: Count the Frequencies
Now, we will count how many marks fall into each class interval:

1. **For the interval 0 - 10**:
- Marks: 8, 9, 7
- Frequency: 3

2. **For the interval 10 - 20**:
- Marks: 15, 10, 16, 17, 19, 11
- Frequency: 6

3. **For the interval 20 - 30**:
- Marks: 20, 20, 24, 27, 25, 28, 21
- Frequency: 7

4. **For the interval 30 - 40**:
- Marks: 30, 30, 36, 38, 37, 31, 40
- Frequency: 7

5. **For the interval 40 - 50**:
- Marks: 44, 47, 47, 41
- Frequency: 4

### Step 4: Construct the Frequency Table
Now, we can construct the frequency table based on the intervals and their corresponding frequencies:

| Class Interval | Frequency |
|----------------|-----------|
| 0 - 10 | 3 |
| 10 - 20 | 6 |
| 20 - 30 | 7 |
| 30 - 40 | 7 |
| 40 - 50 | 4 |

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

| Class Interval | Frequency |
|----------------|-----------|
| 0 - 10 | 3 |
| 10 - 20 | 6 |
| 20 - 30 | 7 |
| 30 - 40 | 7 |
| 40 - 50 | 4 |