Construct a frequency distribution table from the following cumulative frequency distribution :
`{:("Calss Interval","Cumulative Frequency"),(10-19,8),(20-29,19),(30-39,23),(40-49,30):}`

Answer

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

### Step 1: Write down the class intervals and cumulative frequencies.
We have the following data:
- Class Intervals: 10-19, 20-29, 30-39, 40-49
- Cumulative Frequencies: 8, 19, 23, 30

### Step 2: Create a table with three columns: Class Interval, Cumulative Frequency, and Frequency.
We will set up our table as follows:

| Class Interval | Cumulative Frequency | Frequency |
|----------------|----------------------|-----------|
| 10-19 | 8 | |
| 20-29 | 19 | |
| 30-39 | 23 | |
| 40-49 | 30 | |

### Step 3: Calculate the frequency for each class interval.
- **Frequency for the first class interval (10-19)**: This is the same as the cumulative frequency for the first class interval, which is 8.

- **Frequency for the second class interval (20-29)**: This is calculated by subtracting the cumulative frequency of the first class interval from the cumulative frequency of the second class interval:
\[ \text{Frequency} = 19 - 8 = 11 \]

- **Frequency for the third class interval (30-39)**: This is calculated by subtracting the cumulative frequency of the second class interval from the cumulative frequency of the third class interval:
\[ \text{Frequency} = 23 - 19 = 4 \]

- **Frequency for the fourth class interval (40-49)**: This is calculated by subtracting the cumulative frequency of the third class interval from the cumulative frequency of the fourth class interval:
\[ \text{Frequency} = 30 - 23 = 7 \]

### Step 4: Fill in the frequency column in the table.
Now, we can fill in the frequency values in the table:

| Class Interval | Cumulative Frequency | Frequency |
|----------------|----------------------|-----------|
| 10-19 | 8 | 8 |
| 20-29 | 19 | 11 |
| 30-39 | 23 | 4 |
| 40-49 | 30 | 7 |

### Final Frequency Distribution Table
Thus, the final frequency distribution table is:

| Class Interval | Cumulative Frequency | Frequency |
|----------------|----------------------|-----------|
| 10-19 | 8 | 8 |
| 20-29 | 19 | 11 |
| 30-39 | 23 | 4 |
| 40-49 | 30 | 7 |