Consider the following statements
I Mean is independent of change in scale and changes in origin
II. Variance is independent of change in scale bur not in origin Which of the above statements is/are correct?

Options

A. A. 1only
B. B. 2 only
C. C. Both I and II
D. D. Neither I nor II

Answer

To solve the question regarding the correctness of the statements about the mean and variance, we can analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding the Mean**:
- The mean (average) of a dataset is calculated by summing all the values and dividing by the number of values.
- When we change the scale (e.g., multiplying all values by a constant) or change the origin (e.g., adding a constant to all values), the mean will change accordingly.
- **Conclusion**: The first statement, "Mean is independent of change in scale and changes in origin," is **false**.

2. **Understanding the Variance**:
- Variance measures the spread of a set of values around the mean. It is calculated by averaging the squared differences from the mean.
- When we change the scale (e.g., multiplying all values by a constant), the variance will also change because the distances from the mean will be scaled.
- However, when we change the origin (e.g., adding a constant to all values), the distances from the mean remain the same, and thus the variance does not change.
- **Conclusion**: The second statement, "Variance is independent of change in scale but not in origin," is also **false** because variance is dependent on change in scale.

3. **Final Conclusion**:
- Since both statements are false, the correct answer is that neither statement is correct.

### Final Answer:
Neither statement I nor statement II is correct.