Choose the incorrect statement out of the following :-

Options

A. Every measurement by any measuring instrument has some errors
B. Every calculated physical quantity that is based on measured values has some error
C. A measurement can be more accurat but less precision and vice versa.
D. The percentage error is different from relative error

Answer

To determine the incorrect statement from the provided options, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement Analysis**:
- **Statement 1**: "Each measurement by any measuring instrument has some error."
- **Explanation**: This statement is true. All measuring instruments have inherent errors due to limitations in their design, manufacturing, and usage. Therefore, it is impossible to achieve a measurement with zero error.

2. **Statement Analysis**:
- **Statement 2**: "Every calculated physical quantity that is based on the measured value has some errors."
- **Explanation**: This statement is also true. Any physical quantity derived from measurements will carry the errors from those measurements. Thus, it is impossible to have a calculated value that is completely error-free.

3. **Statement Analysis**:
- **Statement 3**: "A measurement can have more accuracy but less precision and vice versa."
- **Explanation**: This statement is true as well. Accuracy and precision are independent concepts. A measurement can be accurate (close to the true value) but not precise (not consistent), and it can be precise (consistent) but not accurate (not close to the true value).

4. **Statement Analysis**:
- **Statement 4**: "Percentage error is different from relative error."
- **Explanation**: This statement is false. Percentage error and relative error are essentially the same concept, as both express the error relative to the true value, often represented as a percentage. Therefore, this is the incorrect statement.

### Conclusion:
The incorrect statement among the options provided is **Statement 4**: "Percentage error is different from relative error."

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