Construct a frequency table for the following ages (in years) of 30 students using equal class intervals, one of them being 9-12, where 12 is not included.
18, 12, 7, 6, 11, 15, 21, 9, 8, 13, 15, 17, 22, 19, 14, 21, 23, 8, 12, 17, 15, 6, 18, 23, 22, 16, 9, 21, 11, 16.

Answer

To construct a frequency table for the ages of 30 students using equal class intervals, we will follow these steps:

### Step 1: Identify the Range of Ages
First, we need to identify the minimum and maximum ages from the given data. The ages provided are:
18, 12, 7, 6, 11, 15, 21, 9, 8, 13, 15, 17, 22, 19, 14, 21, 23, 8, 12, 17, 15, 6, 18, 23, 22, 16, 9, 21, 11, 16.

- **Minimum Age**: 6
- **Maximum Age**: 23

### Step 2: Define Class Intervals
We need to create equal class intervals. One of the intervals is given as 9-12 (where 12 is not included). We will create the following intervals:
1. 6 to 9
2. 9 to 12
3. 12 to 15
4. 15 to 18
5. 18 to 21
6. 21 to 24

### Step 3: Tally the Frequencies
Next, we will count how many ages fall into each of these intervals.

- **6 to 9**: Ages are 6, 7, 8, 8, 9 → **Frequency = 5**
- **9 to 12**: Ages are 9, 11, 11, 12 → **Frequency = 4**
- **12 to 15**: Ages are 12, 13, 14, 15, 15 → **Frequency = 4**
- **15 to 18**: Ages are 15, 15, 15, 17, 17 → **Frequency = 5**
- **18 to 21**: Ages are 18, 18, 19, 21, 21, 21 → **Frequency = 6**
- **21 to 24**: Ages are 21, 21, 22, 22, 23, 23 → **Frequency = 6**

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

| Class Interval | Frequency |
|----------------|-----------|
| 6 - 9 | 5 |
| 9 - 12 | 4 |
| 12 - 15 | 4 |
| 15 - 18 | 5 |
| 18 - 21 | 6 |
| 21 - 24 | 6 |
| **Total** | **30** |

### Step 5: Verify the Total Frequency
Finally, we can verify that the total frequency adds up to 30:
5 + 4 + 4 + 5 + 6 + 6 = 30.