Three students measured the mass of a product of combustion. They recorded measurements of 5.14 g, 5.16 g, and 5.17 g. If the known mass of the product is 5.30 g, how would you describe the students’ measurements?
-
A
Accurate
-
B
Precise
-
C
Both accurate and precise
-
D
Neither accurate nor precise
The students’ measurements are precise.
Precision refers to how close repeated measurements are to one another, regardless of whether they are close to the true or accepted value. In this case, the three measurements (5.14 g, 5.16 g, and 5.17 g) are very close together, showing strong consistency. However, they are noticeably different from the known true mass of 5.30 g, which means they are not accurate. This pattern commonly indicates a systematic error, such as an improperly calibrated balance.
A) Accurate
Accuracy describes how close a measurement is to the true or accepted value. The true mass is 5.30 g, while all three measurements are between 5.14 g and 5.17 g. This is a difference of about 0.13–0.16 g from the true value, which is significant in laboratory measurement. Because the results are not close to 5.30 g, they are not accurate.
B) Precise
Precision describes how close measurements are to each other when repeated under the same conditions. The three values differ by only 0.03 g (from 5.14 g to 5.17 g), which is a very small range. This shows that the students were consistent in their technique and measurement method. Even though the results are not accurate, they are clearly precise, making this the correct answer.
C) Both accurate and precise
For measurements to be both accurate and precise, they must be close to each other and close to the true value. Although these measurements are close to one another, they are not close to 5.30 g. Therefore, they cannot be described as both accurate and precise.
D) Neither accurate nor precise
This option would apply if the measurements were widely scattered and far from the true value. In this case, the measurements are tightly grouped, showing good precision. Therefore, this option is incorrect.
Conclusion
The students produced measurements that are very consistent with one another but not close to the known true mass. This means their results are precise but not accurate. Therefore, the correct answer is B) Precise.

Topic Flashcards
Click to FlipMeasurements of 5.14 g, 5.16 g, and 5.17 g are all consistently lower than a known value of 5.30 g. Are these measurements best described as accurate, precise, or both?
Precise, but not accurate. They are close to each other (precise) but not close to the true value (not accurate).
What is the term for the quality of measurements when they are tightly clustered together, like 5.14, 5.16, and 5.17, regardless of their distance from a known value?
Precision. Precision describes the repeatability or consistency of measurements with each other.
True value: 5.30 g. Measured values: 5.14 g, 5.16 g, 5.17 g. What type of error (random or systematic) does this consistent under-measurement most likely indicate?
Systematic error. A consistent bias, like an uncalibrated scale, shifts all results away from the true value in the same way.
If three measurements are 5.14 g, 5.16 g, and 5.17 g, their average is about 5.16 g. If the true value is 5.30 g, does taking this average fix the problem of inaccuracy?
No. Averaging precise but biased data gives you a more reliable estimate of the wrong value. It confirms the inaccuracy.
A set of measurements is precise but not accurate. To correct this, should you focus on improving your technique or checking your instrument's calibration?
Check the instrument's calibration. Poor technique typically causes scatter (low precision). A consistent offset suggests a systematic error in the tool.