Determine the area of a flat piece of metal according to the data in the table b
ID: 1878524 • 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·am units. For example: Area- 3.2·0.2 Length, cm Width, cm 6.2 6.5 63 6.4 6.7 7.2 7.5 7.6 7.4 7.0 7.3 (a) Determine the mean, standard deviation, and the standard deviation of the mean for the measurements. Hint: Use Logger Pro to help you make the calculetions. Enter your mean values to at tleast four decimal places, and enter your standard deviations to at least five decimal places Dimension Mean Value, m |Standard Deviation, m Standard Deviation of the Mean, m Length, m 0.0648 | 00023 0009X Width, m 0.0733 00022 0008 X (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-04754 Xm2 AA 0000007m2 (c) Report the results 1. Report error with 1 significant figure. 2. 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 shouid not match but the number of the decimal places must.) 80Explanation / Answer
Ans (a):
Length, m
Width, m
0.068
0.072
0.062
0.075
0.065
0.076
0.063
0.074
0.064
0.070
0.067
0.073
Mean
0.0648
0.0733
Std
0.00232
0.00216
Std of the mean
0.00095
0.00088
Ans (b):
Area = L ´ B = 0.0648 ´ 0.0733 = 0.00475 m2
Length = 0.0648 ± 0.00095 m = (0.0648 ± 1.47%) m
Width = 0.0733 ± 0.00088 m = (0.0733 ± 1.20%) m
Area = (0.00475 ± 2.67%)m2 = 0.00475 ± 0.00013 m
Ans (c):
Length = 0.0648 ± 0.0009 m
Width = 0.0733 ± 0.0009 m
Area = 0.00475 ± 0.0001 m2
Ans (d):
The measurements are precise as the spread in the data is less. But, its accuracy can’t be determined as the true value is not given.
So, The measurements are precise. However, it cannot be said for sure whether or not the measurements are accurate.
Length, m
Width, m
0.068
0.072
0.062
0.075
0.065
0.076
0.063
0.074
0.064
0.070
0.067
0.073
Mean
0.0648
0.0733
Std
0.00232
0.00216
Std of the mean
0.00095
0.00088
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