Question

A student takes three measurements of the mass of an object. If the actual mass is \(8.54 \mathrm{~g}\), indicate whether each set of measurements is precise but not accurate, accurate but not precise, both accurate and precise, or neither accurate nor precise: (a) \(6.38 \mathrm{~g}, 9.23 \mathrm{~g}, 4.36 \mathrm{~g}\) (b) \(8.53 \mathrm{~g}, 8.59 \mathrm{~g}, 8.55 \mathrm{~g}\) (c) \(9.53 \mathrm{~g}, 8.54 \mathrm{~g}, 7.54 \mathrm{~g}\) (d) \(6.25 \mathrm{~g}, 6.27 \mathrm{~g}, 6.26 \mathrm{~g}\)

Short answer

(a) Neither accurate nor precise (b) Both accurate and precise (c) Neither accurate nor precise (d) Precise but not accurate

Step-by-step solution

(a) Analyzing the first set of measurements: 6.38 g, 9.23 g, 4.36 g

First, compare these measurements to the actual mass of 8.54 g. The measured values are quite far from the actual mass, so the set is not accurate. Next, consider the precision by looking at how close these measured values are to each other. The variations between the measurements are quite significant, meaning that the set is not precise. Therefore, this set is neither accurate nor precise.

(b) Analyzing the second set of measurements: 8.53 g, 8.59 g, 8.55 g

Compare these measurements to the actual mass of 8.54 g. The measured values are very close to the actual mass, so the set is accurate. Additionally, these measured values are very close to each other, indicating that the set is precise. Therefore, this set is both accurate and precise.

(c) Analyzing the third set of measurements: 9.53 g, 8.54 g, 7.54 g

Compare these measurements to the actual mass of 8.54 g. The measured value 8.54 g is equal to the actual mass, but the other two values differ significantly. Thus, this set is not considered accurate. The variations between these measurements are also significant, meaning that the set is not precise. Therefore, this set is neither accurate nor precise.

(d) Analyzing the fourth set of measurements: 6.25 g, 6.27 g, 6.26 g

Compare these measurements to the actual mass of 8.54 g. The measured values are quite far from the actual mass, so the set is not accurate. However, these measured values are very close to each other, indicating that the set is precise. Therefore, this set is precise but not accurate.

Key concepts

Scientific Measurement

Understanding scientific measurement is pivotal in various scientific fields, as it provides a standardized way of quantifying physical quantities. Each measurement comes with two vital components: dimension, typically in a unit like grams for mass or meters for length, and uncertainty, which accounts for the limits of the measuring process.

With scientific measurement, we inherently deal with a degree of error—which could stem from limitations in the instrument's precision or from the observer's interpretation of the data. To interpret measurements reliably, students need to understand both their precision and accuracy. Recognizing and recording the measurements as well as potential errors allows for consistency and validity in scientific investigations.

Importance of Consistency

Consistently measured data enables comparison and replication in scientific experiments. Without a standard method of measurement, the results would become meaningless as they would lack a common point of reference.

Accuracy vs Precision

The terms 'accuracy' and 'precision' might seem similar but they describe different attributes of measurement. Accuracy refers to how close a measured value is to the actual (true) value, while precision is about the reproducibility of measurements—in other words, how close multiple measurements are to each other, regardless of their closeness to the actual value.

For example, if you were throwing darts, accuracy would mean hitting the bullseye (the true value), whereas precision reflects how tightly the darts group together on the board, even if they are not near the bullseye. In scientific terms, a set of measurements could be precise without being accurate if they are all close to one another but far from the actual value. Likewise, a single measurement could be accurate if it's close to the true value, even if other measurements are scattered.

Visualizing Accuracy and Precision

To visualize this concept, imagine a series of dots representing measured values on a target. Accurate but not precise measurements would scatter around the bullseye, while precise but not accurate measurements would cluster away from it. An ideal scenario reflects both accuracy and precision, where measurements cluster around the bullseye.

Experimental Error

Experimental error encompasses all the factors that contribute to the differences between a measured value and the true value. These errors can be categorized into two main types: systematic errors and random errors.

Systematic errors are consistent and predictable inaccuracies that occur in the measurement process, often due to faulty equipment or a flawed experimental design. For instance, if a scale is improperly calibrated and consistently reads 0.5g less than the actual mass, that contributes to a systematic error.

Random Errors

On the other hand, random errors are unpredictable and vary from one measurement to another, arising from unpredictable fluctuations. Factors such as slight variations in experimental conditions or observer perception can introduce random errors. While systematic errors bias the results in one direction, random errors can be reduced by taking multiple measurements and averaging them.

Experiments are designed to minimize these errors to enhance the reliability of the results. Understanding and mitigating experimental error is crucial to achieving both precision and accuracy in scientific measurement.