Determine the area of a flat piece of metal according to the data in the table b
ID: 1878505 • Letter: D
Question
Determine the area of a flat piece of metal according to the data in the table below. The answer will need to be correctly stated as: (mean value ± m) units. For example: Area = (3.2 ±0.2 cm2).
Determine the mean, standard deviation, and the standard deviation of the mean for the measurements. (Hint: Use Logger Pro to help you make the calculations. Enter your mean values to at least four decimal places, and enter your standard deviations to at least five decimal places.)
(b)
Use the mean values of length and width reported in the table above to calculate the estimated area of the table. Propagate the error in the value of estimated area. (Note: In order to propagate the error in the estimated area, the error (or standard deviation of the mean) in length and width should be found first. Enter your answers to at least three significant figures.)
A= .004038984 m2
A= m2
Report the results.
Report error with 1 significant figure.
Report the mean value with the same number of the decimal places as in the error. (Note: The number of significant figures in the mean value and in the error should not match but the number of the decimal places must.)
L ± L=
mW ± W=
mA ± A=
Can you say if the measurements are accurate and/or precise? (Use your reported values to determine this answer.) HINT
The measurements are both accurate and precise.
The measurements are accurate, but not precise.
The measurements are precise, but not accurate.
The measurements are neither accurate nor precise.
The measurements are precise. However, it can not be said for sure whether or not the measurements are accurate.
The measurements are not precise. However, it can not be said for sure whether or not the measurements are accurate.
Length, cm Width, cm 5.8 7.3 5.5 7.1 5.7 7.0 5.3 7.4 5.2 7.5 5.6 7.6Explanation / Answer
Standard deviation of mean, L ±0.000939
Standard deviation of mean, W ±0.000943
A = 0.004038984*(0.000939/0.0552)^2 + (0.000943/0.07317)^2
2.89361.661
A = 0.0000857 m2
A = 0.857 cm2
L±L = 0.0552±0.000939
W±W = 0.07317±0.000943
A±A = 0.004038984±0.0000857
The measurements are accurate but not precise.
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