Precision and Accuracy in Measurements

1. Definitions

1.1 Precision

  • Degree of agreement between repeated measurements of the same quantity
  • Focuses on consistency and repeatability of results
  • Indicates reliability and reproducibility of the measurement process

1.2 Accuracy

  • How close a measured value is to the true or accepted value
  • Measures the absence of systematic errors or biases
  • Focuses on closeness to the true value, regardless of reproducibility

2. Characteristics

2.1 Precision

  • Indicated by little variation or scatter in repeated measurements
  • Does not necessarily imply accuracy
  • Example: A scale that consistently gives the same weight within 0.1 kg margin

2.2 Accuracy

  • Indicated by closeness to the true value
  • Does not necessarily imply precision
  • Example: A thermometer that reads close to the actual temperature, even if readings vary

3. Comparison

PrecisionAccuracyDescription
HighHighMeasurements are consistent and close to the true value
HighLowMeasurements are consistent but systematically off from the true value
LowHighMeasurements are scattered but average close to the true value
LowLowMeasurements are scattered and far from the true value

4. Analogy: Dart Throwing

  • Accurate: Darts land close to the center (bullseye)
  • Precise: Darts are tightly grouped
  • Scenarios:
  • 1. Accurate and precise: Darts hit bullseye and are tightly grouped
  • 2. Accurate but not precise: Darts near center but scattered
  • 3. Precise but not accurate: Darts tightly grouped but off-center

5. Importance in Measurements

Both precision and accuracy are desirable

Achieving both requires:

  • Careful calibration of instruments
  • Control of experimental conditions
  • Consideration of error sources

6. Practice Question

Q: Books in a library were counted one by one. There were a total of 57,000 books.

a) How many significant digits are there in the result?

b) Will the result change if the books are measured in packets of 10?

A:

a) 3 significant digits (5, 7, and the first 0)

b) Yes, the result would change to 57,000 ± 10 books, affecting precision