Physics 1 Lecture Notes: Accuracy and Precision

Learning Objectives

• Differentiate between accuracy and precision.
• Differentiate between random errors and systematic errors.
• Solve problems involving accuracy and precision.

Importance of the Topic

• Context in Science: Validity of measurements in experiments is crucial.
• Usage: Essential for determining the validity of the data obtained from trials.

Definitions

Accuracy

• Definition: Closeness of a measured value to the true value.
• Key Points:
  • Present error less than or equal to 10% indicates accuracy.
  • Hitting the target value or deriving the true accepted measurement.
• Example:
  • Dart board analogy: Hitting the bull's eye means being accurate.

Precision

• Definition:
  • Agreement of results with one another, nearness to the value, and consistency in results.
• Example:
  • Dart pins clustering together but not on the target indicates precision.

Testing Accuracy and Precision

Accuracy Test

• Formula for Percent Error:

  [ ext{Percent Error} = \frac{|\text{Actual Value} - \text{Experimental Value}|}{\text{Actual Value}} \times 100 % ]

• Interpretation:

  • Greater than 10% = inaccurate
  • Less than or equal to 10% = accurate.

Precision Test

• Deviation Test:
  • Absolute Deviation:
    [ |x - \bar{x}| ]
  • Relative Deviation:
    [ \frac{\text{Average Absolute Deviation}}{\text{Mean Value}} \times 100 ]
• Interpretation:
  • Greater than 10% = not precise
  • Less than or equal to 10% = precise.

Types of Errors

Random Errors

• Definition: Unpredictable changes during measurements.
• Examples: Electronic noise, temperature variations, wind.

Systematic Errors

• Definition: Errors from measuring instruments or experimental design.
• Effect: Limits accuracy of results.

Percent Difference

• Definition: Measures how far apart different measurement values are, indicating precision.

• Formula:

  [ ext{Percent Difference} = \frac{|\text{Measurement 1} - \text{Measurement 2}|}{\frac{\text{Measurement 1} + \text{Measurement 2}}{2}} \times 100 ]

Example Problems

Example 1: Percent Difference Calculation

• Problem: Two trials determine the latent heat of vaporization of water. Values: 532 cal/g and 536 cal/g.
• Calculation:
  [ \text{Percent Difference} = \frac{|532 - 536|}{\frac{532 + 536}{2}} \times 100 = 0.74% ]

Example 2: Accuracy and Precision Using Excel

• Problem: Determine accuracy and precision of rubber ball volume measurement (true value 50 cc).
• Steps:
  • Calculate average volume.
  • Calculate absolute deviations.
  • Compute average absolute deviation.
  • Find relative deviation and percent error.
• Results:
  • Average Volume: 50.14 cc
  • Percent Error: 0.28% (accurate)
  • Relative Deviation: 1.79% (precise).

Conclusion

• The experimenters achieved both accuracy and precision based on the data obtained.