Given below are the marks obtained by 24 students in an examination :
`{:(18 17 16 24 25 19 41 22),(32 42 44 21 43 26 28 40),(29 30 37 27 49 27 34 31):}`
Taking class intervals 10 - 20, 20 - 30, ............... , 50 - 60, make a frequency table for the above distribution.

Answer

To create a frequency table for the given marks obtained by 24 students, we will follow these steps:

### Step 1: Identify the Class Intervals
We will define the class intervals based on the given range. The intervals are:
- 10 - 20
- 20 - 30
- 30 - 40
- 40 - 50
- 50 - 60

### Step 2: Count the Frequencies
Next, we will count how many marks fall into each class interval. We will go through the list of marks and tally them in the appropriate intervals.

The marks obtained by the students are:
`18, 17, 16, 24, 25, 19, 41, 22, 32, 42, 44, 21, 43, 26, 28, 40, 29, 30, 37, 27, 49, 27, 34, 31`

Now, we will categorize these marks into the defined intervals:

- **10 - 20**: 18, 17, 16, 19 → 4 marks
- **20 - 30**: 24, 25, 22, 32, 21, 26, 28, 29, 30 → 9 marks
- **30 - 40**: 37, 34, 31, 40 → 4 marks
- **40 - 50**: 41, 42, 44, 43, 49 → 5 marks
- **50 - 60**: No marks → 0 marks

### Step 3: Create the Frequency Table
Now, we will create the frequency table using the counts from the previous step.

| Class Interval | Tally Marks | Frequency |
|----------------|-------------|-----------|
| 10 - 20 | |||| | 4 |
| 20 - 30 | ||||| |||| | 9 |
| 30 - 40 | |||| | 4 |
| 40 - 50 | ||||| | 5 |
| 50 - 60 | | 0 |
| **Total** | | **24** |

### Step 4: Verify the Total Frequency
Finally, we verify that the total frequency adds up to 24:
4 (10-20) + 9 (20-30) + 4 (30-40) + 5 (40-50) + 0 (50-60) = 22

### Final Frequency Table
The completed frequency table is:

| Class Interval | Frequency |
|----------------|-----------|
| 10 - 20 | 4 |
| 20 - 30 | 9 |
| 30 - 40 | 4 |
| 40 - 50 | 5 |
| 50 - 60 | 0 |
| **Total** | **24** |