Two students determine the percentage of iron in a sample as a laboratory exercise. The true percentage is 34.43%. The students’ results for three determinations are as follows: 1. 34.44, 34.41, 34.46 2. 34.51, 34.56, 34.48 b. Precision can be judged by examining the average of the deviations from the average value for that data set. (Calculate the average value for each data set; then calculate the average value of the absolute deviations of each measurement from the average.) Which set is more precise?

Verified step by step guidance

1. Calculate the average value for the first data set: (34.44 + 34.41 + 34.46) / 3.
2. Calculate the average value for the second data set: (34.51 + 34.56 + 34.48) / 3.
3. Determine the absolute deviation of each measurement from the average for the first data set: |measurement - average|.
4. Determine the absolute deviation of each measurement from the average for the second data set: |measurement - average|.
5. Calculate the average of the absolute deviations for each data set and compare them to determine which set is more precise.

Key Concepts

Precision

Precision refers to the consistency of repeated measurements, indicating how close the values are to each other, regardless of their proximity to the true value. In this context, it is assessed by calculating the average of the absolute deviations of each measurement from the average value of the data set. A smaller average deviation signifies higher precision.

Average (Mean)

The average, or mean, is calculated by summing all the values in a data set and dividing by the number of values. It provides a central value that represents the data set, which is essential for comparing the precision of different sets of measurements. In this case, the average values of the two data sets will be compared to evaluate their precision.

Absolute Deviation

Absolute deviation measures the distance between each data point and the mean, expressed as a positive value. It is calculated by taking the absolute value of the difference between each measurement and the average. This concept is crucial for determining how spread out the measurements are around the mean, which directly informs the assessment of precision.