The class marks of a distribution are 12, 18, 24, 30. Find the class interval.

Answer

To find the class intervals from the given class marks of a distribution (12, 18, 24, 30), we will follow these steps:

### Step 1: Find the Class Size
The class size can be determined by calculating the difference between two consecutive class marks.

- Class Size = Class Mark (2) - Class Mark (1)
- Class Size = 18 - 12 = 6

### Step 2: Calculate Half of the Class Size
Next, we need to find half of the class size to determine how much to subtract and add to the class marks.

- Half of Class Size = Class Size / 2
- Half of Class Size = 6 / 2 = 3

### Step 3: Determine the First Class Interval
Using the first class mark (12), we will calculate the first class interval.

- Lower Limit = First Class Mark - Half of Class Size
- Lower Limit = 12 - 3 = 9
- Upper Limit = First Class Mark + Half of Class Size
- Upper Limit = 12 + 3 = 15

Thus, the first class interval is **9 to 15**.

### Step 4: Determine the Second Class Interval
Now, we will calculate the second class interval using the second class mark (18).

- Lower Limit = Second Class Mark - Half of Class Size
- Lower Limit = 18 - 3 = 15
- Upper Limit = Second Class Mark + Half of Class Size
- Upper Limit = 18 + 3 = 21

Thus, the second class interval is **15 to 21**.

### Step 5: Determine the Third Class Interval
Next, we will calculate the third class interval using the third class mark (24).

- Lower Limit = Third Class Mark - Half of Class Size
- Lower Limit = 24 - 3 = 21
- Upper Limit = Third Class Mark + Half of Class Size
- Upper Limit = 24 + 3 = 27

Thus, the third class interval is **21 to 27**.

### Step 6: Determine the Fourth Class Interval
Finally, we will calculate the fourth class interval using the fourth class mark (30).

- Lower Limit = Fourth Class Mark - Half of Class Size
- Lower Limit = 30 - 3 = 27
- Upper Limit = Fourth Class Mark + Half of Class Size
- Upper Limit = 30 + 3 = 33

Thus, the fourth class interval is **27 to 33**.

### Final Answer
The required class intervals are:
1. 9 to 15
2. 15 to 21
3. 21 to 27
4. 27 to 33

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