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Let's break down the steps to calculate the requested quantities from the given frequency distribution table:

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

### i. Relative Frequency
Relative frequency is calculated as the frequency of each class divided by the total frequency.

- Total number of students (total frequency) = \( 4 + 6 + 10 + 18 + 12 + 10 = 60 \)

Relative frequency for each class is:
- \( \frac{4}{60} = 0.067 \)
- \( \frac{6}{60} = 0.100 \)
- \( \frac{10}{60} = 0.167 \)
- \( \frac{18}{60} = 0.300 \)
- \( \frac{12}{60} = 0.200 \)
- \( \frac{10}{60} = 0.167 \)

### ii. Class Mark
The class mark (midpoint of each class interval) is calculated by averaging the lower and upper limits of each class.

Class marks for each interval:
- For 10-20: \( \frac{10 + 20}{2} = 15 \)
- For 20-30: \( \frac{20 + 30}{2} = 25 \)
- For 30-40: \( \frac{30 + 40}{2} = 35 \)
- For 40-50: \( \frac{40 + 50}{2} = 45 \)
- For 50-60: \( \frac{50 + 60}{2} = 55 \)
- For 60-70: \( \frac{60 + 70}{2} = 65 \)

### iii. Width of Class Interval
The width of a class interval is the difference between the upper and lower limits of any class.

- Class interval width: \( 20 - 10 = 10 \)

### iv. Cumulative Frequency Distribution
Cumulative frequency is the running total of frequencies up to each class.

- For 10-20: \( 4 \)
- For 20-30: \( 4 + 6 = 10 \)
- For 30-40: \( 10 + 10 = 20 \)
- For 40-50: \( 20 + 18 = 38 \)
- For 50-60: \( 38 + 12 = 50 \)
- For 60-70: \( 50 + 10 = 60 \)

### Summary:

| Marks   | Frequency | Relative Frequency | Class Mark | Cumulative Frequency |
|---------|-----------|--------------------|------------|----------------------|
| 10-20   | 4         | 0.067              | 15         | 4                    |
| 20-30   | 6         | 0.100              | 25         | 10                   |
| 30-40   | 10        | 0.167              | 35         | 20                   |
| 40-50   | 18        | 0.300              | 45         | 38                   |
| 50-60   | 12        | 0.200              | 55         | 50                   |
| 60-70   | 10        | 0.167              | 65         | 60                   |

Would you like more details on any part of this solution?

Here are some related questions:
1. How would you calculate the mean from this table?
2. What is the median class for this distribution?
3. How would you compute the variance of this data?
4. Can you explain the concept of cumulative relative frequency?
5. How is the mode of a frequency distribution table determined?

**Tip:** The cumulative frequency distribution helps identify percentiles and is useful in finding the median of grouped data.

For the following frequency distribution table, calculate the relative frequency, class mark, width of the class interval, and cumulative frequency distribution for the given data.

This page explains how to calculate the relative frequency, class mark, and cumulative frequency distribution for a frequency distribution table. Learn to break down statistical data for marks ranging from 10-70, with detailed step-by-step calculations. Suitable for high school students (Grades 9-12).

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