The measure of accuracy is

Options

A. absolute error
B. relative error
C. percentage error
D. both 2 and 3

Answer

To determine the measure of accuracy, we need to understand the concepts of absolute error, relative error, and percentage error. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand Absolute Error
- **Definition**: Absolute error is the difference between the measured value and the actual value. It tells us how far off a measurement is from the true value.
- **Calculation**: If you have a set of measurements (x1, x2, x3, x4), the absolute error for each measurement can be calculated as:
- \( |x - x_i| \) for each measurement \( x_i \), where \( x \) is the actual value.

### Step 2: Calculate Mean Absolute Error
- **Definition**: The mean absolute error (MAE) is the average of all absolute errors.
- **Calculation**:
- \( \text{MAE} = \frac{|x - x_1| + |x - x_2| + |x - x_3| + |x - x_4|}{4} \)

### Step 3: Understand Relative Error
- **Definition**: Relative error is the absolute error divided by the actual value, which gives a sense of how significant the error is relative to the size of the measurement.
- **Calculation**:
- \( \text{Relative Error} = \frac{\text{MAE}}{x} \)

### Step 4: Calculate Percentage Error
- **Definition**: Percentage error is simply the relative error expressed as a percentage.
- **Calculation**:
- \( \text{Percentage Error} = \left(\frac{\text{MAE}}{x}\right) \times 100 \)

### Step 5: Determine the Measure of Accuracy
- **Conclusion**:
- Accuracy is determined by how close a measurement is to the actual value. Both relative error and percentage error provide insights into accuracy, as they indicate how small the error is relative to the actual value.
- Therefore, the measure of accuracy is represented by relative error and percentage error.

### Final Answer
- The measure of accuracy is **relative error and percentage error**.