Overview
This lesson explains the differences between precision and accuracy, introduces true value, scatter, systematic error, and random error, and describes how these concepts apply to scientific measurements and experiments.
Precision and Scatter
- Precision is the degree to which repeated measurements are close to each other.
- Scatter refers to how spread out data points are in a set of results.
- Low scatter means high precision; high scatter means low precision.
Accuracy and True Value
- Accuracy measures how close results are to the true (accepted or actual) value.
- True value is the standard or accepted value for a measurement (e.g., water boils at 100°C).
Types of Measurement Examples
- Low precision and low accuracy: results are scattered and far from the true value.
- Low precision and high accuracy: results are scattered but average equals the true value.
- High precision and low accuracy: results are close together but far from true value, indicating systematic error.
- High precision and high accuracy: results are close together and near the true value.
Systematic and Random Error
- Systematic error affects all measurements consistently, often due to flaws in equipment or method.
- Random error affects measurements unpredictably and arises from uncontrollable variables or human factors.
- Systematic errors shift all results; random errors cause scatter.
Identifying and Reducing Errors
- Systematic errors are identified by repeating experiments with different methods or equipment and comparing results.
- Random errors are minimized by increasing the number of trials and averaging results (increasing sample size).
- Increased repetition does not eliminate random error but reduces its impact on results.
Student Measurement Example
- Four students measured water’s boiling point; results showed varying combinations of precision and accuracy:
- Student 1: low precision, low accuracy.
- Student 2: high precision, low accuracy (systematic error likely).
- Student 3: high precision, high accuracy.
- Student 4: low precision, high accuracy.
Key Terms & Definitions
- Precision — how close repeated measurements are to each other.
- Scatter — the spread of data points in a set of results.
- Accuracy — how close a measurement is to the true value.
- True Value — the accepted or correct value for a quantity.
- Systematic Error — consistent error affecting all measurements in the same way.
- Random Error — unpredictable error causing variation in measurements.
Action Items / Next Steps
- Practice identifying types of errors in sample data sets.
- Repeat key experiments with alternative apparatus to check for systematic errors.
- Plan to increase sample size in future experiments to lessen random error effects.