Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows:
0 1 2 2 1 2 3 1 3 0
1 3 1 1 2 2 0 1 2 1
3 0 0 1 1 2 3 2 2 0
Prepare a frequency distribution table for the data given above.

Answer

To prepare a frequency distribution table for the number of heads obtained from tossing three coins 30 times, we will follow these steps:

### Step 1: Collect the Data
We have the following data from the experiment:
```
0, 1, 2, 2, 1, 2, 3, 1, 3, 0,
1, 3, 1, 1, 2, 2, 0, 1, 2, 1,
3, 0, 0, 1, 1, 2, 3, 2, 2, 0
```

### Step 2: Count the Frequency of Each Outcome
We will count how many times each possible outcome (0, 1, 2, 3 heads) occurs in the data.

- **Count of 0 heads**:
- The occurrences of 0 are: 0, 0, 0, 0, 0, 0 (total = 6)

- **Count of 1 head**:
- The occurrences of 1 are: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (total = 10)

- **Count of 2 heads**:
- The occurrences of 2 are: 2, 2, 2, 2, 2, 2, 2, 2, 2 (total = 9)

- **Count of 3 heads**:
- The occurrences of 3 are: 3, 3, 3, 3, 3 (total = 5)

### Step 3: Create the Frequency Distribution Table
Now we can organize the counts into a frequency distribution table:

| Number of Heads | Frequency |
|------------------|-----------|
| 0 | 6 |
| 1 | 10 |
| 2 | 9 |
| 3 | 5 |
| **Total** | **30** |

### Step 4: Verify the Total
We can verify that the total frequency adds up to 30:
- 6 (for 0 heads) + 10 (for 1 head) + 9 (for 2 heads) + 5 (for 3 heads) = 30

### Final Frequency Distribution Table
The final frequency distribution table is:

| Number of Heads | Frequency |
|------------------|-----------|
| 0 | 6 |
| 1 | 10 |
| 2 | 9 |
| 3 | 5 |
| **Total** | **30** |