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Let's solve the given frequency distribution table by calculating the following:

### 1. Relative Frequency
Relative frequency is calculated as the frequency of each class divided by the total number of students.

### 2. Class Mark
Class mark (midpoint) is calculated as the average of the lower and upper boundaries of each class interval.

### 3. Width of Class Interval
The width of the class interval is the difference between the upper and lower boundaries of a class interval.

### 4. Cumulative Frequency Distribution
Cumulative frequency is calculated by adding the frequency of each class to the sum of the frequencies of all preceding classes.

Now, let's calculate each one:

#### Given Data:
- Marks: 10-20, 20-30, 30-40, 40-50, 50-60, 60-70
- Number of Students: 4, 6, 10, 18, 12, 10

#### Total Number of Students:
\[
4 + 6 + 10 + 18 + 12 + 10 = 60
\]

### Calculations:

| Marks | Frequency | Relative Frequency | Class Mark | Width of Interval | Cumulative Frequency |
|-------|-----------|--------------------|------------|-------------------|----------------------|
| 10-20 | 4         | \( \frac{4}{60} = 0.0667 \) | \( \frac{10+20}{2} = 15 \) | \( 20 - 10 = 10 \) | 4                    |
| 20-30 | 6         | \( \frac{6}{60} = 0.1 \)   | \( \frac{20+30}{2} = 25 \) | \( 30 - 20 = 10 \) | 4 + 6 = 10            |
| 30-40 | 10        | \( \frac{10}{60} = 0.1667 \) | \( \frac{30+40}{2} = 35 \) | \( 40 - 30 = 10 \) | 10 + 10 = 20          |
| 40-50 | 18        | \( \frac{18}{60} = 0.3 \)  | \( \frac{40+50}{2} = 45 \) | \( 50 - 40 = 10 \) | 20 + 18 = 38          |
| 50-60 | 12        | \( \frac{12}{60} = 0.2 \)  | \( \frac{50+60}{2} = 55 \) | \( 60 - 50 = 10 \) | 38 + 12 = 50          |
| 60-70 | 10        | \( \frac{10}{60} = 0.1667 \) | \( \frac{60+70}{2} = 65 \) | \( 70 - 60 = 10 \) | 50 + 10 = 60          |

Let me know if you need further explanations or have any questions. 

### Questions to Explore:
1. How would you calculate the mean of the distribution?
2. What is the importance of relative frequency in data analysis?
3. How can you use cumulative frequency to find the median class?
4. Can you explain the significance of class width in data interpretation?
5. How would you graphically represent this data?

### Tip:
When working with frequency distributions, always double-check that your cumulative frequency adds up to the total number of observations to ensure accuracy.

For the following Frequency Distribution table, calculate: i. Relative Frequency, ii. Class Mark, iii. Width of Class Interval, iv. Cumulative Frequency Distribution.

Learn how to calculate the relative frequency, class mark, width of class intervals, and cumulative frequency distribution from a frequency distribution table with data on student marks. This problem covers statistical concepts such as frequency distributions and is suitable for high school students.

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