Activity 3.8 Precision and Accuracy of Measurement



Activity 3.8 Precision and Accuracy of MeasurementIntroductionThis concept of random and systematic errors is related to the precision and accuracy of measurements. Precision characterizes the system's probability of providing the same result every time a sample is measured (related to random error). Accuracy characterizes the system's ability to provide a mean close to the true value when a sample is measured many times (related to systematic error). We can determine the precision of a measurement instrument by making repeated measurements of the same sample and calculating the standard deviation of those measurements. However, we will not be able to correct any single measurement due to a low precision instrument. Simply stated, the effects of random uncertainties can be reduced by repeated measurement, but it is not possible to correct for random errors.We can determine the accuracy of a measurement instrument by comparing the experimental mean of a large number of measurements of a sample for which we know the "true value" of the characteristic of the sample. A sample for which we know the "true value" would be our calibration standard. We may also need to characterize the accuracy of the measurement instrument by observing historical trends in the distribution of measured values for the calibration standard (this allows for determining the systematic error expected from environmental effects, etc.). The effects of systematic uncertainties cannot be reduced by repeated measurements. The cause of systematic errors may be known or unknown. If both the cause and the value of a systematic error are known, it can be corrected for by "subtracting" the known deviation. However, there will still remain a systematic uncertainty component associated with this correction.EquipmentEngineering notebookGauge blockDial caliperProcedureFive students are asked to measure the length of the same bolt. The accepted estimated measurement of the bolt is 64.1 mm. Each student measured the bolt with a ruler and a dial caliper the results are below.RulerDial caliperStudent 164.1mm64.2157 mmStudent 264.2 mm64.1583 mmStudent 364.2 mm64.1592 mmStudent 464.1mm64.2538 mmStudent 564.0mm64.2320mmFind the mean of measurements recorded by the ruler and by the dial caliper.Mean of ruler = ________________Mean of dial caliper = ________________ Find the range of the measurements recorded by the ruler and by the dial caliperRange of ruler = ________________Range of dial caliper = ________________Create one dot plot with both sets of data on it, the rule and dial caliper. Use different colors or shapes to differentiate between the ruler and dial caliper data.Which student’s tool is more accurate? Explain.Give a reason that could cause the _____________ (dial caliper, ruler) data to not be accurate.Which student’s tool is more precise Show your work mathematically or explain. The company that produces these wooden blocks, claimed the lengths are 0.75" ±.03” We will test this claim.What does 0.75" ± .03” mean?The cubes must have lengths between _____________ and ____________ inches.Find the length of 14 blocks wooden blocks. Take your measurements from packet 3.6What percentage of the blocks are within 0.75" ± .03” Show work.Create a dot plot with the above data. Label the axesAre these blocks produced by this company accurate? Explain and show work mathematically.Are these blocks produced by this company precise? Explain and show work mathematicallyConclusionWhat is the difference between accuracy and precision?Which measuring device is more precise, a ruler or dial caliper? Explain.Why is it important for engineers’ measurements to be both accurate and precise? ................
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