Concept explainers
You and your lab partner are asked to determine the density of an aluminum bar. The mass is known accurately (to four significant figures). You use a simple metric ruler to measure its dimensions and obtain the results for Method A. Your partner uses a precision micrometer and obtains the results for Method B
The accepted density of aluminum is 2.702 g/cm3.
- (a) Calculate the average density for each method. Should all the experimental results be included in your calculations? If not, justify any omissions.
- (b) Calculate the percent error for each method's average value.
- (c) Calculate the standard deviation for each set of data.
- (d) Which method's average value is more precise? Which method is more accurate?
(a)
Interpretation: The average density for each method and the justifications for omissions has to be given.
Concept introduction:
Precision: Is a measurement indicates how well several determination of the same quantity agree.
Accuracy: Is the agreement of a measurement with the accepted value of the quantity.
Percent error: The difference between measured result and the accepted value.
Answer to Problem 21RPS
Average value for Method A is
Average value for Method B is
For B, the
Explanation of Solution
Average density Value for Method A and B:
Hence, the average for method A and B are obtained as shown above. B, the
(b)
Interpretation: The percent error for each method’s average value has to be calculated.
Concept introduction:
Precision: Is a measurement indicates how well several determination of the same quantity agree.
Accuracy: Is the agreement of a measurement with the accepted value of the quantity.
Percent error: The difference between measured result and the accepted value.
Answer to Problem 21RPS
Method A: error
Method B: error
Explanation of Solution
Percent error for Method A and B:
From the above calculation, the percent errors are obtained as shown above.
(c)
Interpretation: The standard deviation for each set of data.
Concept introduction:
Precision: Is a measurement indicates how well several determination of the same quantity agree.
Accuracy: Is the agreement of a measurement with the accepted value of the quantity.
Percent error: The difference between measured result and the accepted value.
Answer to Problem 21RPS
Method A: standard deviation
Method B: (including all data points) standard deviation
Method B: (excluding the
Explanation of Solution
Standard deviation for method A:
Standard deviation for method B:
Standard deviation excluding the
(d)
Interpretation:
The method that has the more precise value and accurate has to be given.
Concept introduction:
Precision: Is a measurement indicates how well several determination of the same quantity agree.
Accuracy: Is the agreement of a measurement with the accepted value of the quantity.
Percent error: The difference between measured result and the accepted value.
Explanation of Solution
Method B average is both more precise and more accurate so long as the
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