General Physics 1 - Lesson 2: Accuracy and Precision

Target Competencies

• Differentiate accuracy from precision
• Differentiate random errors from systematic errors
• Estimate errors from multiple measurements of physical quantities

Key Concepts

• Good measurement = Low or limited error
• Measurements are not always accurate; errors occur due to various factors
• Accuracy: Closeness of a measurement to the accepted value
• Precision: Agreement of several measurements made in the same way

Errors in Measurement

• Errors are unavoidable and can be:
  • Random Errors:
    • Unpredictable and inconsistent
    • No discernible pattern
    • Example: Variable readings from a measuring device due to conditions like lighting
  • Systematic Errors:
    • Consistent and repeatable errors
    • Often due to flawed measuring devices or methods
    • Requires modification of the measurement process to correct

Factors Affecting Measurement Errors

1. Type of measuring device used
2. Measurement methods (user knowledge)
3. Environmental conditions

Example: Dart Game

• Illustration of Accuracy and Precision:
  1. Trial 1: Poor accuracy and poor precision (darts scattered)
  2. Trial 2: Good accuracy, poor precision (darts near target but scattered)
  3. Trial 3: Poor accuracy, high precision (darts clustered but far from target)
  4. Trial 4: Good accuracy and high precision (darts near and clustered around target)

Accuracy Calculation

• Absolute Error (AE):
  • AE = |Observed Value (O) - Accepted Value (A)|
• Percentage Error:
  • Percent Error = (AE / A) x 100
• Percentage of Accuracy:
  • Accuracy = 100% - Percentage of Error

Example Calculation

• Experiment: Dropped stone from 5-story building, measured time = 3 seconds, observed acceleration = 9.7 m/s²
• Accepted acceleration = 9.8 m/s²
• Calculations:
  • AE = |9.7 - 9.8| = 0.1
  • Percentage Error = (0.1 / 9.8) x 100 = 1.02%
  • Percentage of Accuracy = 100% - 1.02% = 98.98%

Precision Calculation

• Absolute Deviation (AD):
  • AD = |O - Mean|
• Percentage of Deviation:
  • Percent Deviation = (AD / Mean) x 100
• Percentage of Precision:
  • Precision = 100% - Percentage of Deviation

Example Calculation

• Experiment: Three trials of a ball falling 3 meters: 0.80 s, 0.79 s, 0.77 s
  • Mean = (0.80 + 0.79 + 0.77) / 3 = 0.787 s
  • Calculate AD for each trial, then total AD, then average AD
  • Calculate Percentage of Deviation and Percentage of Precision

Summary

• Accuracy = Closeness to true value
• Precision = Consistency among multiple measurements

Activities for Students

1. Activity A: Calculate percentage of accuracy for John and Sally's aluminum density measurements.
2. Activity B: Calculate percentage of precision for Tokyo's robot football measurements across four trials.

• Review previous slides or videos for additional understanding.
• Good luck!