Notes on the Lecture: Accuracy vs. Precision

Introduction to the Story of William Tell

• William Tell forced into a challenge by a corrupt lord.
• Challenge: shoot an apple off his son's head.
• Two variations of the story considered.

Variation 1: Stolen Crossbow

• Lord hires a bandit to steal William's crossbow.
• William borrows an inferior crossbow.
• Practice shots cluster beneath the bullseye.
• Has time to correct the aim before the challenge.

Variation 2: Shaky Hand

• William doubts his skills before the challenge.
• Develops a tremor in his hand.
• Practice shots cluster randomly around the apple.
• Hits the apple occasionally but lacks certainty.

Key Terms: Accuracy vs. Precision

• Accuracy: Closeness to the correct result.
  • Improved by properly calibrated tools and training.
• Precision: Consistency of getting the same result using the same method.
  • Improved by finely incremented tools that reduce estimation.

Examples from Variations

• Stolen Crossbow:
  • Precision without accuracy (same wrong result).
• Shaky Hand:
  • Accuracy without precision (results cluster around the correct answer but not reliably).

Importance in Scientific Endeavors

• Low accuracy or precision can suffice in daily tasks.
• Engineers and researchers require high levels of accuracy and precision.

Investments in Precision

• Required for factories and labs to decrease uncertainty.
• Improvements can be expensive; managers must assess acceptable levels of uncertainty.

NASA's Mars Missions

• NASA lacks exact landing predictions for probes.
• Extensive calculations and variable measurements needed for landing predictions.
• Landing Ellipse:
  • Viking Lander (1976): 62 x 174 miles.
  • Curiosity Lander (2012): 4 miles x 12 miles.
  • Technology and simulations allowed targeting high-interest areas.

Conclusion

• Striving for accuracy is essential, but precision reflects certainty in achieving results.
• Both principles are necessary for successful endeavors, including space missions.