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.
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
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.
To calculate the percentage error, you can use the following formula:
Percentage Error = (Experimental Value - Actual Value) / Actual Value * 100
In this case, the experimental values are 14.91%, 14.89%, 14.88%, and 14.90%. The actual value is 14.90%.
Calculating the percentage error for each value:
Percentage Error for 14.91% = (14.91% - 14.90%) / 14.90% * 100 = 0.67%
Percentage Error for 14.89% = (14.89% - 14.90%) / 14.90% * 100 = -0.07%
Percentage Error for 14.88% = (14.88% - 14.90%) / 14.90% * 100 = -0.13%
Percentage Error for 14.90% = (14.90% - 14.90%) / 14.90% * 100 = 0%
To calculate the precision, you can use the range of data. The range is the difference between the maximum and minimum values. In this case, the range is 14.91% - 14.88% = 0.03%
Now, let's analyze the results:
The percentage error is close to zero for all values except one, which has a percentage error of -0.13%. Overall, the average percentage error is very small.
The precision is determined by the range, which is 0.03%. Generally, a smaller range indicates higher precision.
Based on these calculations, we can conclude that the results are precise but not accurate. Although the percentage error is small, there is still some deviation from the actual value. However, the precision is high since the range is small.