Accuracy and Precision

Accuracy

• Definition: the closeness of a measurement to the true or accepted value.

• Key idea: reflects correctness with respect to the true value.

Precision

• Definition: the degree of agreement between successive measurements using a given instrument (how close measurements are to each other).

• Key idea: can be high or low independent of accuracy.

Relationship between Accuracy and Precision

• They are related but different concepts.

• A measurement can be highly precise but not accurate.

• A measurement can be accurate but not precise.

• Often described together to assess data quality.

Visual Analogy: Darts

• Bull’s-eye = the true value.

• Accuracy: how close darts are to the bull’s-eye.

• Precision: how close darts are to each other.

• Scenarios:

  • High accuracy & high precision: darts clustered at the bull’s-eye.

  • High precision, low accuracy: darts clustered together but away from the bull’s-eye.

  • High accuracy, low precision: darts near the bull’s-eye but spread out.

  • Low accuracy & low precision: darts spread out and away from the bull’s-eye.

Analyzing Accuracy and Precision

• Best data: high accuracy and high precision.

• Range is used to assess precision across data sets.

• Range formula: $\text{Range} = x<em>{\max} - x</em>{\min}$

Example: 75.0 g standard sample

• Trials:

  • Trial 1: $74.8\ \text{g}$

  • Trial 2: $74.7\ \text{g}$

  • Trial 3: $74.9\ \text{g}$

• Conclusion: measurements are precise (values are close to each other) and accurate (close to the true value $75.0\ \text{g}$).

Temperature Readings (Five Days)

• Forecasted temperatures show high precision (values are close to one another).

• Actual temperatures indicate lower accuracy relative to the forecast.

• Takeaway: high precision does not guarantee high accuracy.

Group Precision: 150 g Mass Measurements

• Data:

  • Group 1: $142.7, 145.8, 149.5, 143.4, 148.9$

  • Group 2: $149.7, 148.5, 148.1, 149.5, 150.2$

  • Group 3: $135.9, 140.8, 151.2, 145.7, 146.3$

• Ranges:

  • Group 1: $6.8$

  • Group 2: $1.6$

  • Group 3: $15.3$

• Conclusion: Group 2 is most precise (smallest range); Group 3 has the lowest precision (largest range).

Mnemonic

• ACcurate is Correct (or Close to real value).

• PRecise is Repeating (or Repeatable values).

Importance in Chemistry

• Accurate and precise measurements ensure data quality and reliable chemical preparations.

• Proper measurement tools are used to quantify substances for product quality.