A student performed an analysis of a sample for its calcium content and got the following results: 14.91%, 14.89%, 14.88%, and 14.90% The actual amount of calcium in the sample is 14.90%. Calculate the percentage error and precision. Comment on the precision and accuracy of the results.

Question

The percentage error is close to zero

The results are precise and accurate

The results are accurate but not precise

The results are precise but not accurate

Answer 1

The percentage error is (|14.90-14.89|/14.90) x 100% = 0.067%

The precision can be determined by calculating the variance or standard deviation of the results. Assuming the student did not make multiple measurements for each trial, we can only calculate the precision relative to the mean:

Precision = (Range/mean) x 100% = [(14.91-14.88)/14.90] x 100% = 0.201%

The percentage error indicates that the results are very close to the actual value of calcium in the sample, which suggests that the results are accurate. The precision, on the other hand, is relatively low, indicating that there is some variability between the measurements. However, it is important to note that this precision calculation is limited by the small sample size, and if more measurements were taken, the precision could likely be improved. Overall, the results are accurate but not highly precise.