Construct a frequency table from the following data
`{:("Marks","No of students"),("less than" 10,6),("less than" 20,15),("less than" 30,30),("less than" 40,39),("less than" 50,53),("les than" 60,70):}`

Answer

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

### Step 1: Identify the Class Intervals and Frequencies
We are given cumulative frequencies (less than certain marks) and need to determine the actual frequencies for each class interval.

### Step 2: Define Class Intervals
The class intervals based on the given data will be:
- 0 to 10
- 10 to 20
- 20 to 30
- 30 to 40
- 40 to 50
- 50 to 60

### Step 3: Calculate Frequencies
1. **For the interval 0 to 10:**
- Cumulative frequency (less than 10) = 6
- Frequency = 6

2. **For the interval 10 to 20:**
- Cumulative frequency (less than 20) = 15
- Frequency = 15 - 6 = 9

3. **For the interval 20 to 30:**
- Cumulative frequency (less than 30) = 30
- Frequency = 30 - 15 = 15

4. **For the interval 30 to 40:**
- Cumulative frequency (less than 40) = 39
- Frequency = 39 - 30 = 9

5. **For the interval 40 to 50:**
- Cumulative frequency (less than 50) = 53
- Frequency = 53 - 39 = 14

6. **For the interval 50 to 60:**
- Cumulative frequency (less than 60) = 70
- Frequency = 70 - 53 = 17

### Step 4: Construct the Frequency Table
Now we can summarize the data in a frequency table:

| Class Interval | Frequency |
|----------------|-----------|
| 0 to 10 | 6 |
| 10 to 20 | 9 |
| 20 to 30 | 15 |
| 30 to 40 | 9 |
| 40 to 50 | 14 |
| 50 to 60 | 17 |

### Final Frequency Table
The final frequency table is as follows:

| Marks (Class Interval) | No of Students (Frequency) |
|------------------------|---------------------------|
| 0 to 10 | 6 |
| 10 to 20 | 9 |
| 20 to 30 | 15 |
| 30 to 40 | 9 |
| 40 to 50 | 14 |
| 50 to 60 | 17 |