Marks obtained by some students of a class are 36, 37, 31, 42, 23, 38, 17, 18, 35, 25, 29 and 35.
The difference of the mean and the range of the data is :

Question

Accepted Answer

To determine the difference between the mean and the range of the given data, we need to follow these steps:

1. **Calculate the Mean:**
   - The mean is the average of all the numbers.
   - First, sum up all the marks: 
     $$
     36 + 37 + 31 + 42 + 23 + 38 + 17 + 18 + 35 + 25 + 29 + 35 = 366
     $$
   - There are 12 students, so the mean is:
     $$
     \text{Mean} = \frac{366}{12} = 30.5
     $$

2. **Calculate the Range:**
   - The range is the difference between the highest and lowest values in the data set.
   - The highest mark is 42, and the lowest mark is 17.
   - Therefore, the range is:
     $$
     \text{Range} = 42 - 17 = 25
     $$

3. **Calculate the Difference between the Mean and the Range:**
   - The difference is calculated as:
     $$
     \text{Difference} = \text{Mean} - \text{Range} = 30.5 - 25 = 5.5
     $$

Thus, the difference between the mean and the range of the data is 5.5, which corresponds to Option 3.

**Explanation of Why Other Options are Incorrect:**

- **Option 1 (4.5):** This option is incorrect because the calculated difference is 5.5, not 4.5. The mean and range calculations clearly show that the difference is 5.5.

- **Option 2 (5):** This option is incorrect because the precise difference between the mean and the range is 5.5, not 5. The calculations demonstrate that the mean is 30.5 and the range is 25, leading to a difference of 5.5.

- **Option 4 (6):** This option is incorrect because the difference calculated is 5.5, not 6. The arithmetic operations confirm that the correct difference is 5.5.

Therefore, based on the calculations and logical reasoning, Option 3 is the correct answer.