Overview
This lecture explains how to calculate error and percent error in measurements, illustrating their significance in evaluating the accuracy of results.
Calculating Error
- Error is the difference between the measured value and the actual value (Error = Measured Value - Actual Value).
- A positive error means the measurement is above the actual value; a negative error means it is below.
- Include the plus or minus sign to indicate the direction of the error.
Examples of Error Calculation
- Example: 503.5 ft - 500.0 ft = +3.5 ft error (above actual value).
- Example: 502.8 ft - 500.0 ft = +2.8 ft error.
- Example: 497.4 ft - 500.0 ft = -2.6 ft error (below actual value).
Understanding Percent Error
- Percent error compares the size of the error to the actual value to determine its significance.
- Formula: Percent Error = (|Error| ÷ Actual Value) × 100%.
- Always use the absolute value of the error for percent error calculations.
Examples of Percent Error Calculation
- Example: (|3.5| ÷ 500.0) × 100% = 0.7% percent error.
- Example: (|2.6| ÷ 500.0) × 100% = 0.52% percent error.
- The same error value can represent a larger or smaller percent error depending on the size of what's being measured.
Importance of Percent Error
- Percent error helps indicate whether a measurement error is significant relative to the size of what is being measured.
- A small absolute error can be a large percent error if the object measured is small, and vice versa.
Combining Error and Percent Error Formulas
- The percent error formula can be written as: Percent Error = (|Measured Value - Actual Value| ÷ Actual Value) × 100%.
Key Terms & Definitions
- Error — The difference between the measured value and the actual value.
- Percent Error — The absolute value of the error divided by the actual value, times 100%, showing the error’s relative size.
- Absolute Value — The non-negative value of a number, ignoring the sign.
Action Items / Next Steps
- Practice calculating error and percent error with sample measurement data.
- Review the percent error formula and be able to apply it to various scenarios.