Precision and Accuracy
When we make a measurement in the laboratory, it is important to evaluate its quality. To do this, we use two key concepts: Precision and Accuracy.
Precision: Refers to the consistency or reproducibility of a set of measurements.
Accuracy: Refers to how close a measurement is to the true or accepted value.
To better understand these concepts, let's use the analogy of throwing darts at a dartboard. The goal is to hit the bullseye, which represents the true value. Precision and accuracy can be visualized by observing how the darts land on the board.
In science, it is important for measurements to be both precise and accurate.
Two students, Raffaella and Barbara, measured the temperature of boiling water, which, under 1 atmosphere of pressure, should be exactly 100°C. Each student made 10 temperature measurements, shown below as red dots for Raffaella and blue dots for Barbara:
The average of Raffaella's measurements is 100.1°C, and the average of Barbara's measurements is also 100.1°C. This means the accuracy of their measurements is identical. However, the figure shows that Raffaella's measurements are more tightly clustered, indicating better precision.
Think: What factors might cause one set of measurements to be more variable than another?
Hint: Consider differences in experimental technique, instrument quality, or environmental conditions.
In science, precision is often expressed by including an uncertainty with measured values. For example, Raffaella would report a boiling point of 100.1 ± 0.3°C, while Barbara would report 100.1 ± 1.4°C. This uncertainty is referred to as a random error, which reflects the variability in repeated measurements. Random error is different from a systematic error, which is the difference between the average measured value and the true value. In this case, both Raffaella and Barbara had a systematic error of 0.1°C, as the true boiling point of water is 100°C.
Think: What could be some causes of systematic error in a laboratory setting?
Hint: Consider calibration issues with instruments or consistent procedural biases.
If the measurement uncertainty cannot be explicitly specified, the precision of a measured number can still be approximated using the number of significant figures. For instance, Raffaella would report a boiling point of 1.001 x 102 °C, while Barbara would report 1.00 x 102 °C. Raffaella's result has four significant figures, whereas Barbara's has only three, reflecting the difference in their precision.