A student performed an analysis of a sample forits 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 results are precise and accurate
The results are accurate but not precise
The results are precise but not accurate
The percentage error is close to zero
and the precision is high, as all the measurements are very close to each other.
To calculate the percentage error, we can use the formula:
Percentage Error = [(Measured Value - True Value) / True Value] x 100
Using the given data, we get:
Percentage Error = [(14.89% - 14.90%) / 14.90%] x 100
Percentage Error = (-0.01% / 14.90%) x 100
Percentage Error = -0.067% (rounded to two decimal places)
Since the percentage error is very close to zero, we can say that the results are accurate. The precision can be calculated using the range, which is the difference between the highest and lowest values:
Range = 14.91% - 14.88%
Range = 0.03%
Since the range is very small, we can say that the results are precise. Therefore, we can conclude that the results are both accurate and precise.
To calculate the percentage error, you can use the formula:
Percentage Error = ((Measured Value - Actual Value) / Actual Value) * 100
Using the given data, the measured values are 14.91%, 14.89%, 14.88%, and 14.90%, and the actual value is 14.90%.
Let's calculate the percentage error for each measurement:
Percentage Error 1 = ((14.91 - 14.90) / 14.90) * 100 = 0.07%
Percentage Error 2 = ((14.89 - 14.90) / 14.90) * 100 = -0.07%
Percentage Error 3 = ((14.88 - 14.90) / 14.90) * 100 = -0.13%
Percentage Error 4 = ((14.90 - 14.90) / 14.90) * 100 = 0
To calculate the precision, you need to consider the range of values. In this case, the range is the difference between the highest and lowest measured values:
Range = 14.91% - 14.88% = 0.03%
To analyze the precision, you can compare the range to the average value:
Precision = (Range / Average Value) * 100
Average Value = (14.91 + 14.89 + 14.88 + 14.90) / 4 = 14.895%
Precision = (0.03 / 14.895) * 100 = 0.2%
Based on the calculated percentage error and precision, we can conclude that the results are precise but not accurate. The percentage error is close to zero, indicating a high level of accuracy. However, the precision is relatively low, as the range of values is small compared to the average value.