Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52%. The students’ results for three determinations are as follows: (1) 22.52, 22.48, 22.54 (2) 22.64, 22.58, 22.62 (a) Calculate the average percentage for each set of data and state which set is the more accurate based on the average.

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Calculate the average percentage for the first set of data by adding the values 22.52, 22.48, and 22.54, then divide the sum by the number of values, which is 3.

Calculate the average percentage for the second set of data by adding the values 22.64, 22.58, and 22.62, then divide the sum by the number of values, which is 3.

Compare the calculated average of each set to the true percentage value of 22.52% to determine which set is more accurate.

The set with the average percentage closest to the true percentage of 22.52% is considered more accurate.

Discuss the concept of accuracy in measurements, which refers to how close a measured value is to the true value, and how this applies to the results obtained by the students.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Accuracy vs. Precision

Accuracy refers to how close a measured value is to the true value, while precision indicates the consistency of repeated measurements. In this context, the accuracy of the students' results can be assessed by comparing their averages to the true percentage of lead, 22.52%. A set of measurements can be precise but not accurate if they cluster together but are far from the true value.

Calculating Averages

To find the average percentage of lead in each set of data, sum the individual measurements and divide by the number of measurements. This statistical method provides a central value that represents the data set, allowing for a straightforward comparison between the two sets of results.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. When reporting the average percentage, it is important to consider the significant figures of the original measurements to ensure that the final result reflects the precision of the data. This practice helps maintain the integrity of the measurements and their reliability.

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Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52%. The students' results for three determinations are as follows: (1) 22.52, 22.48, 22.54 (2) 22.64, 22.58, 22.62 (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?

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