A student performed an analysis of a sample for its calcium content and got the following results:

14.92% , 14.91%, 14.88% , 14.91%.

The actual amount of calcium in the sample is 15.70%. What conclusion can you draw about the accuracy and precision of these results?

precision is good

... the four results are within 4 parts in 1490 of each other ... about .3%

accuracy is not so hot
... the error is ... (14.9 - 15.7) / 15.7
... about 5%

Am not clear about your answer

What conclusion can be you draw about the accuracy and precision of these results

What conclusion can you draw about the accuracy and precision of these results?

To assess the accuracy and precision of the results, we can calculate the mean and standard deviation of the measurements.

First, let's calculate the mean:
Mean = (14.92% + 14.91% + 14.88% + 14.91%) / 4 = 14.90%

The mean represents the average calcium content measured and gives an indication of accuracy.

Next, let's calculate the standard deviation (SD) as a measure of precision. The formula to calculate the sample standard deviation is as follows:

SD = sqrt((∑(xi - x̄)²) / (n - 1))

Where:
- xi represents each individual measurement
- x̄ is the mean of the measurements
- n is the total number of measurements

For our case, the calculations are as follows:

SD = sqrt(((14.92% - 14.90%)² + (14.91% - 14.90%)² + (14.88% - 14.90%)² + (14.91% - 14.90%)²) / (4 - 1))

SD = sqrt((0.0004 + 0.0001 + 0.0004 + 0.0001) / 3)

SD = sqrt(0.0002 / 3) = sqrt(0.0000667) ≈ 0.0082 = 0.82%

The standard deviation gives an indication of how much the measurements deviate from the mean and represents the precision of the results.

Now, with the mean and standard deviation calculated, we can draw conclusions regarding accuracy and precision:

1. Accuracy: The mean of the measurements (14.90%) deviates from the actual amount of calcium (15.70%). Therefore, the results are not accurate, indicating a systematic error or bias in the measurements.

2. Precision: The standard deviation of the measurements (0.82%) represents the average amount of variation in the measurements. A smaller standard deviation indicates higher precision. In this case, the standard deviation is relatively low, suggesting that the measurements are precise and consistent.

In summary, the results are precise but not accurate, indicating that the measurements are consistent but are systematically biased.