Construct a frequency distribution table for the following data, taking class-intervals `4-6, 6-8`, ............., `14-16`.
`11.5, 6.3, 7.8, 9.2, 10.5,`
`4.5, 6, 8.3, 12.5, 15.8,`
`7.4, 5.3, 8.4, 15.2, 8.9,`
`9.8, 8.25, 6.5, 5.8, 10.5,`
`14.2, 15.3, 11.7, 9.9, 8.8,`
`6.6, 4.3, 4.7, 9.4, 10.1,`
`15.5, 14.4, 12.2, 7.7, 5.5`.

Answer

To construct a frequency distribution table for the given data with the specified class intervals (4-6, 6-8, 8-10, 10-12, 12-14, 14-16), we will follow these steps:

### Step 1: Identify the Class Intervals
The class intervals are:
- 4 to 6
- 6 to 8
- 8 to 10
- 10 to 12
- 12 to 14
- 14 to 16

### Step 2: Count the Frequencies
We will count how many data points fall into each class interval.

1. **Class Interval 4-6**:
- Data points: 4.5, 6.0, 5.3, 5.8, 4.3, 4.7
- Count: 6

2. **Class Interval 6-8**:
- Data points: 6.3, 7.8, 6.0, 6.5, 6.6, 7.4, 8.3, 8.4, 8.9, 8.25
- Count: 10

3. **Class Interval 8-10**:
- Data points: 9.2, 9.8, 9.9, 9.4, 8.8, 8.3
- Count: 6

4. **Class Interval 10-12**:
- Data points: 10.5, 10.5, 10.1, 11.5, 11.7, 12.2
- Count: 6

5. **Class Interval 12-14**:
- Data points: 12.5, 14.2, 14.4
- Count: 3

6. **Class Interval 14-16**:
- Data points: 15.8, 15.2, 15.3, 15.5
- Count: 4

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

| Class Interval | Frequency |
|----------------|-----------|
| 4 - 6 | 6 |
| 6 - 8 | 10 |
| 8 - 10 | 6 |
| 10 - 12 | 6 |
| 12 - 14 | 3 |
| 14 - 16 | 4 |

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

| Class Interval | Frequency |
|----------------|-----------|
| 4 - 6 | 6 |
| 6 - 8 | 10 |
| 8 - 10 | 6 |
| 10 - 12 | 6 |
| 12 - 14 | 3 |
| 14 - 16 | 4 |