Random Error

Definition

Random error is the unpredictable variation in a measurement that occurs even when the same procedure is followed multiple times. It is caused by uncontrollable factors and cannot be eliminated, but its effects can be reduced through repeated measurements and statistical analysis.

5 Must Know Facts For Your Next Test

1. Random error is caused by uncontrollable factors, such as environmental conditions, instrument sensitivity, and human error, and cannot be eliminated completely.
2. The effects of random error can be reduced by increasing the number of measurements and using statistical analysis techniques, such as calculating the standard deviation or standard error.
3. Random error is often represented by the symbol $\sigma$ and is usually expressed as a range or interval around the measured value.
4. Significant figures are affected by random error, as the number of significant figures in a measurement reflects the precision of the measurement.
5. Repeated measurements can help to identify and quantify random error, as the variation in the measurements will reflect the magnitude of the random error.

Review Questions

• Explain how random error affects the number of significant figures in a measurement.
  • Random error directly impacts the number of significant figures in a measurement. The more precise the measurement, the more significant figures it can include. Measurements with larger random errors will have fewer significant figures, as the uncertainty in the measurement limits the number of digits that can be reliably reported. Conversely, measurements with smaller random errors can include more significant figures, as the uncertainty is reduced. The number of significant figures reflects the precision of the measurement and is a way to communicate the magnitude of the random error.
• Describe how repeated measurements can be used to identify and quantify random error.
  • Performing repeated measurements is a key way to identify and quantify random error. When the same measurement is repeated under the same conditions, the variation in the results reflects the magnitude of the random error. By calculating the standard deviation or standard error of the repeated measurements, you can determine the range or interval within which the true value is likely to fall. This provides a quantitative measure of the random error, which can then be used to assess the reliability and precision of the measurement process.
• Analyze the relationship between random error, precision, and accuracy, and explain how they are interconnected.
  • Random error, precision, and accuracy are closely related concepts in measurement. Random error is the unpredictable variation in a measurement that affects its precision, or the closeness of multiple measurements to each other. Measurements with larger random errors will have lower precision, as the values will be more spread out. Accuracy, on the other hand, refers to how close a measurement is to the true or accepted value. While random error affects precision, it does not necessarily impact accuracy. A measurement can be precise (low random error) but inaccurate (biased by systematic error). Conversely, a measurement can be accurate (close to the true value) but imprecise (high random error). Minimizing both random and systematic errors is essential for achieving high accuracy and precision in measurements.

Related terms

Systematic Error:

Systematic error is a consistent deviation from the true value that is caused by flaws in the measurement process, such as instrument calibration or experimental design.

Precision:

Precision refers to the closeness of multiple measurements to each other, and is a measure of the repeatability or reproducibility of a measurement.

Accuracy:

Accuracy is the closeness of a measurement to the true or accepted value, and is a measure of how well a measurement reflects the actual quantity being measured.