To find the missing values in a cumulative frequency distribution table, you typically need to work with the information given. Here’s a general approach to finding the missing values \(a\), \(b\), \(c\), and \(d\):
1. **Identify the Total Frequency**: The cumulative frequency of the last interval should equal the total number of observations. If the total frequency is given, use it to fill in the final cumulative frequency.
2. **Determine Frequencies from Cumulative Frequencies**:
- The cumulative frequency of a class interval is the sum of the frequencies of all previous intervals and the frequency of the current interval.
- You can calculate the frequency of each interval by subtracting the cumulative frequency of the previous interval from the cumulative frequency of the current interval.
3. **Solve for Missing Values**:
- Use the cumulative frequency values and the given data to set up equations for the missing values and solve them.
Let's apply this to a hypothetical table.
### Hypothetical Cumulative Frequency Distribution Table:
| Class Interval | Frequency | Cumulative Frequency |
|----------------|-----------|----------------------|
| 0-10 | a | 15 |
| 10-20 | b | 45 |
| 20-30 | 20 | 65 |
| 30-40 | c | d |
| 40-50 | 10 | 100 |
### Steps to Solve:
1. **Determine the total frequency** (last cumulative frequency):
- \(d = 100\)
2. **Work backwards to find \(c\)**:
- \(c + 65 = 100 \implies c = 35\)
3. **Find \(b\)** using the cumulative frequency:
- \(b + 15 = 45 \implies b = 30\)
4. **Finally, find \(a\)**:
- The first cumulative frequency is equal to \(a\):
- \(a = 15\)
### Completed Table:
| Class Interval | Frequency | Cumulative Frequency |
|----------------|-----------|----------------------|
| 0-10 | 15 | 15 |
| 10-20 | 30 | 45 |
| 20-30 | 20 | 65 |
| 30-40 | 35 | 100 |
| 40-50 | 10 | 100 |
Make sure to use the specific values given in your problem for an accurate solution. If you provide the actual table values, I can help you more precisely.
