The density of copper is listed as 8.94 g/cm to the third. Two students each make three density determinations of samples of the substance. Student A's results are 7.3 g/mL, 9.4 g/mL, and 8.3 g/mL. Student B's results are 8.4 g/cm to the third, 8.8 g/cm to the third, and 8.0 g/cm to the third. Comparing the two results how close are they in precision and accuracy?
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To compare the precision and accuracy of two sets of results, we need to understand the concepts of precision and accuracy.
Precision refers to the consistency or reproducibility of measurements. A set of measurements is considered precise if the values are close to each other. On the other hand, accuracy refers to how close a measurement is to the true or accepted value.
Let's compare the precision of the two sets of results first. Student A's three density determinations are 7.3 g/mL, 9.4 g/mL, and 8.3 g/mL. The range of these values (9.4 - 7.3 = 2.1) is quite large, indicating low precision.
Student B's three density determinations are 8.4 g/cm³, 8.8 g/cm³, and 8.0 g/cm³. The range of these values (8.8 - 8.0 = 0.8) is smaller than that of Student A's results, suggesting higher precision.
Now, let's assess the accuracy of the measurements. The accepted density of copper is given as 8.94 g/cm³.
For Student A, the average density determination is (7.3 + 9.4 + 8.3) / 3 = 8.33 g/mL. Comparing to the accepted value, there is a discrepancy of 0.61 g/mL, indicating low accuracy.
For Student B, the average density determination is (8.4 + 8.8 + 8.0) / 3 = 8.4 g/cm³. Comparing to the accepted value, there is a discrepancy of 0.54 g/cm³, indicating relatively higher accuracy.
To summarize:
- Student A's results have low precision, as the range of their measurements is large.
- Student A's results have low accuracy, as there is a significant discrepancy from the accepted value.
- Student B's results have higher precision, as the range of their measurements is smaller.
- Student B's results have relatively higher accuracy, as there is a smaller discrepancy from the accepted value.
Therefore, Student B's results are both more precise and more accurate compared to Student A's results.
The average of student B is 8.40 g/cc. The average of student A is 8.33 g/cc.
The range of A is 8.0-8.8 or 0.8 from low to high.
The range of B is 7.3 to 9.4 or 2.1 from low to high.
Which do you think is closest to the accepted value? Which has the most closely spaced values?