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Presentation NameCourse NameUnit # – Lesson #.# – Lesson NameRecording Measurements A measurement always includes a value A measurement always includes units A measurement always involvesuncertaintyAccuracy and Precisionof MeasurementSources of Error in Measurement Potential errors create uncertainty Two sources of error in measurement– Random Error Errors without a predictable pattern E.g., reading scale where actual value is betweenmarks and value is estimated Can be determined by repeated measurements– A measurement is the best estimate of aquantity– A measurement is useful if we can quantifythe uncertaintyUncertainty in Measurements Scientists and engineers often use significantdigits to indicate the uncertainty of ameasurement– A measurement is recorded such that all certain digitsare reported and one uncertain (estimated) digit isreported– Systematic Error Errors that consistently cause measurement valueto be too large or too small E.g., reading from the end of a meter stick insteadof from the zero markProject Lead The Way, Inc.Copyright 20101

Presentation NameCourse NameUnit # – Lesson #.# – Lesson NameUncertainty in MeasurementsUncertainty in Measurement Another (more definitive) method to indicateuncertainty is to use plus/minus notation In some cases the uncertainty from adigital or analog instrument is greater thanindicated by the scale or reading display– Resolution of the instrument is better than theaccuracy Example: Speedometers– Example: 3.84 .05 cm 3.79 true value 3.89 This means that we are certain the truemeasurement lies between 1.19 cm and 1.29 cmUncertainty in Measurement Uncertainty of single measurement How close is this measurement to the true value? Uncertainty dependent on instrument and scale Uncertainty in repeated measurementsHow can we determine, with confidence,how close a measurement is to the truevalue?Accuracy and Precision Accuracy the degree of closeness ofmeasurements of a quantity to the actual (oraccepted) value Precision (repeatability) the degree to whichrepeated measurements show the same result Random error Best estimate is the mean of the valuesHigh AccuracyLow PrecisionProject Lead The Way, Inc.Copyright 2010Low AccuracyHigh PrecisionHigh AccuracyHigh Precision2

Presentation NameCourse NameUnit # – Lesson #.# – Lesson NameAccuracy and PrecisionYour Turn Ideally, a measurement device is both accurateand precise Accuracy is dependent on calibration to astandardTwo students each measure the length of acredit card four times. Student A measureswith a plastic ruler, and student B measureswith a precision measuring instrument calleda micrometer.– Correctness– Poor accuracy results from procedural or equipmentflaws– Poor accuracy is associated with systematic errorsStudent A85.1mm85.0 mm85.2 mm84.9 mm Precision is dependent on the capabilities of themeasuring device and its use– Reproducibility– Poor precision is associated with random errorStudent B85.701 mm85.698 mm85.699 mm85.701 mmYour TurnYour TurnPlot Student A’s data on a number lineStudent A’s data ranges from 85.0 mm to 85.2 mmPlot Student B’s data on a number lineStudent B’s data ranges from 85.298 mm to 85.301 mmStudent B85.301 mm85.298 mm85.299 mm85.301 mmThe accepted length of the credit card is 85.105 mmAcceptedValue85.105Student A85.1mm85.0 mm85.2 mm85.1 mmProject Lead The Way, Inc.Copyright 20103

Presentation NameCourse NameUnit # – Lesson #.# – Lesson NameYour TurnQuantifying AccuracyWhich student’s data is more accurate?The accuracy of a measurement is related tothe error between the measurement valueand the accepted valueStudent AWhich student’s data is more precise?Student BError measured values– accepted valueStudent A85.1mm85.0 mm85.2 mm85.1 mmStudent A:xA 85.10 mmStudent B85.301 mm85.298 mm85.299 mm85.301 mmStudent B:xB 85.2998 mmQuantifying AccuracyQuantifying AccuracyCalculate the error of Student A’s measurementsCalculate the error of Student B’s measurements85.105AcceptedValueProject Lead The Way, Inc.Copyright 2010Error- 0.005Error0.1948xB 85.2998xA 85.10Error- 0.005Error B mean of measured values – accepted valueError B 85.2998 mm – 85.105 mm 0.1948 mmAccepted85.105ValuexA 85.10Error A mean of measured values – accepted valueError A 85.10 mm – 85.105 mm 0.005 mm4

Presentation NameCourse NameUnit # – Lesson #.# – Lesson NameQuantifying AccuracyQuantifying AccuracyCalculate the error of Student B’s measurementsCalculate the error of Student B’s measurementsError 0.1948 0.1948 0.1948xB 85.2998xA 85.10Student AMORE ACCURATEError - 0.005 0.005 0.00585.105Accepted85.105ValueError 0.1948 0.1948 0.1948Error B mean of measured values – accepted valueError B 85.2998 mm – 85.105 mm 0.1948 mmAcceptedValueError - 0.005 0.005 0.005xB 85.2998xA 85.10Error B mean of measured values – accepted valueError B 85.2998 mm – 85.105 mm 0.1948 mmQuantifying PrecisionQuantifying PrecisionPrecision is related to the variation inmeasurement data due to random errors thatproduce differing values when ameasurement is repeatedThe precision of a measurement device canbe related to the standard deviation ofrepeated measurement dataStudent A85.1mm85.0 mm85.2 mm85.1 mmProject Lead The Way, Inc.Copyright 2010Student B85.301 mm85.298 mm85.299 mm85.301 mmStudent A:sA 0.08 mmStudent B:sB 0.0015 mm5

Presentation NameCourse NameUnit # – Lesson #.# – Lesson NameQuantifying PrecisionQuantifying PrecisionUse the empirical rule to express precisionExpress the precision indicated by Student A’sdata at the 68% confidence level True value is within one standard deviation of themean with 68% confidence True value is within two standard deviations of themean with 95% confidence True value is 85.10 0.08 mm with 68%confidence 85.10 0.08 mm true value 85.10 0.08 mm85.02 mm true value 85.18 mmwith 68% confidenceStudent A:xA 85.10 mmsA 0.07 mmQuantifying PrecisionExpress the precision indicated by Student A’sdata at the 95% confidence level True value is 85.10 2(0.08) mm with 95%confidenceThe Statistics of Accuracy and PrecisionALow AccuracyHigh PrecisionBHigh AccuracyHigh Precision 85.10 0.16 mm true value 85.10 0.16 mm84.94 mm true value 85.26 mmwith 95% confidenceStudent A:xA 85.10 mmsA 0.07 mmProject Lead The Way, Inc.Copyright 2010CLow AccuracyLow PrecisionDHigh AccuracyLow Precision6

Presentation NameCourse NameUnit # – Lesson #.# – Lesson NameGauge Blocks (Gage Blocks) A block whose length isprecisely and accuratelyknown Standard basis of comparison Precision measuring devices are oftencalibrated using gauge blocks Calibrate to check or adjust bycomparison to a standardProject Lead The Way, Inc.Copyright 20107

a micrometer. Student A Student B 85.1mm 85.701 mm 85.0 mm 85.698 mm 85.2 mm 85.699 mm 84.9 mm 85.701 mm Your Turn Plot Student A’s data on a number line Student A Student B 85.1mm 85.301 mm 85.0 mm 85.298 mm 85.2 mm 85.299 mm 85.1 mm 85.301 mm Plot Student B’s data on a number line Student B’s data ranges from Your Turn

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