Worksheet-Accuracy and Precision-Final (1)

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Fortis Institute, Port Saint Lucie *

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GMAS125

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Statistics

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Feb 20, 2024

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Science, Measurement, and Uncertainty: Accuracy and Precision Name: Kayla A. De La Cruz Period:1 Date: 9/7/23 ACCURACY AND PRECISION Definitions: Accuracy – how close a measurement is to the goal or target. Precision – how close a measurement is to each other. Precision versus Accuracy: Look at each target and decide whether the “hits” are accurate, precise, both accurate and precise, or neither accurate nor precise: (Note: An accurate “hit” is a bulls eye!) Accurate?: Yes / No Precise?: Yes / No Accurate?: Yes / No Precise?: Yes / No Accurate?: Yes / No Precise?: Yes / No Precision Problems: A group of students worked in separate teams to measure the length of an object. Here are their data: Team 1 Team 2 Team 3 Team 4 Team 5 Team 6 Team 7 2.65 cm 2.75 cm 2.80 cm 2.77 cm 2.60 cm 2.65 cm 2.68 cm • The average length is 2.7 cm. This is the mean or average. • Subtract the highest value from the lowest value: 0.15 cm. This is the range or spread. • Divide this number by 2: 0.075 cm. This is the approximate ± range from the average. • The precision of the measurement can be shown as average ± range.The precision of the measurement was 0.15 ± 0.075 cm. Expressing Errors in Measurement: Demystifying Scientific Data: RET 2006, Rev 2 25

Science, Measurement, and Uncertainty: Accuracy and Precision Scientists often express their uncertainty and error in measurement by giving a percent error. The percent error is defined as: % error = actual value − measured value x 100 Actual value Answer the following four questions. Pay attention to significant figures, and show your work! 1. While doing a lab, a student found the density of a piece of pure aluminum to be 2.85 g/cm 3 . The accepted value for the density of aluminum is 2.70 g/cm 3 . What was the student's percent error? 2.7-2.85/2.7 x 100 2.7-2.85=-0.15 -0.15/2.7= 0.055555 -0.0555x100= -5.5% 2. A student measured the specific heat of water to be 4.29 J/g · C o . The literature value of the specific heat of water is 4.18 J/g · C o . What was the student’s percent error? 4.29-4.18/4.29 x 100 4.29-4.18=0.11 0.11x100=1.21% Precent error: 1.21% 3. A student took a calibrated 200.0 gram mass, weighed it on a laboratory balance, and found it read 196.5 g. What was the student’s percent error? 200-196.5/200x100 200-196.5 =3.5 3.5/200=0.0175 0.0175x100=1.75% Precent error:1.75% Demystifying Scientific Data: RET 2006, Rev 2 26

Science, Measurement, and Uncertainty: Accuracy and Precision 4. Accuracy is often expressed as an average of several measurements. Look at the target to the right. In your opinion, how well do the measurements on the target represent: (Justify your opinion.) a. Accuracy? Being that there were 5 marks the accuracy in this example could be measured as 1/5 because they only hit the desired target once. b. Precision? There isn’t much precision in this example none of the marks were close to each other. Demystifying Scientific Data: RET 2006, Rev 2 27

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