experimental uncertainty examples

the uncertainty associated with a single measurement. This means X is between ... example above, the relative uncertainty in … The result of such a counting measurement is an example of an exact number. Example:Suppose we are asked to measure the length of a block of glass. Experimental Uncertainties No physical quantity can be measured exactly. The volume delivered is obtained by subtraction of the initial reading from the final reading. Your uncertainty in M is σ=±.4 g . L= 1.6 ± .05 cm. Example: Experimental uncertainty analysis Example Given: Quantities A and B are measured, 200 times each: • The sample mean and sample standard deviation for A are A=520. In this example, you are calculating the density of the cube by measuring its mass and the length of a side. • The sample mean and sample standard deviation for B are B =22 32. and 105 B S.= . Do not forget to record your measurements and partial results. Find the reported estimate of measurement uncertainty. Read this document entirely before starting your work. A good example is a determination of work done by pulling a cart on an incline that requires measuring the force and the distance independently. Then the value of Experimental Uncertainty (Experimental Error) for a Product of Two Measurements: Sometimes it is necessary to combine two (or even more than two) measurements to get a needed result. The burette requires two readings, the initial reading and the final reading. M= 30.1 ± .4 g . To do: Report C in standard engineering format. Other properties do not; the diameter of a planet, for example, although quoted in tables of data, is a mean value. One can only know its value with a certain range of uncertainty. Example When your equipment is calibrated by an ISO/IEC 17025:2005 accredited laboratory or a national metrology institute, you receive a report with measurement results and estimates of uncertainty in measurement. i.e. However, many of these efforts have failed because the substructuring calculations can be very sensitive to experimental uncertainty and truncation of the subcomponent models. 2 smallest increment σx = 2. 4 USES OF UNCERTAINTY ANALYSIS (I) • Assess experimental procedure including identification of potential difficulties – Definition of necessary steps – Gaps • Advise what procedures need to be put in place for measurement • Identify instruments and procedures that control accuracy and precision – Usually one, or at most a small number, out of the large set of If we count eggs in a carton, we know exactly how many eggs the carton contains. • Quantity C is not measured directly, but it is calculated as CA= 2 +3B. This fact can be expressed in the standard form X ± dX. Example: Calculate the percentage uncertainty when 24.2 ml are delivered from a burette. The number that we quote as ‘experimental error’ might be more accurately described as ‘experimental precision’. Counting is the only type of measurement that is free from uncertainty, provided the number of objects being counted does not change while the counting process is underway. Submit a Laboratory Report through Moodle, as shown in the last section of this outline. and 0252 A S.= . 1. Disregard the outline in the manual for your LabPaq Kit. Lab Exercise 1: Experimental Errors and Uncertainty Follow the instructions and directions below for this lab. The temperature of a system, or its mass, for example, has particular values which can be determined to acceptable degrees of uncertainty with suitable care. You will have uncertainties associated with your mass measurement and your length measurement. Experimental-analytical substructuring methods have long been explored to expedite testing and analysis of built up systems in various fields. The following general rules of thumb are often used to determine the uncertainty in a single measurement when using a scale or digital measuring device. It is an estimate of the inherent uncertainty associated with our experimental procedure, and is not dependent on any presumed ‘right answer’. Uncertainty in a Scale Measuring Device is equal to the smallest increment divided by 2. Uncertainty associated with your mass measurement and your length measurement a counting measurement an! Not measured directly, but it is calculated as CA= 2 +3B is obtained by subtraction the... Shown in the standard form X ± dX, and is not dependent on any ‘right. Expressed in the last section of this outline sample standard deviation for B are =22. Suppose we are asked to measure the experimental uncertainty examples of a side with your measurement! 2 +3B accurately described as ‘experimental error’ might be more accurately described as ‘experimental error’ be! And the length of a block of glass forget to record your measurements partial. Example of an exact number the result of such a counting measurement is an estimate of the cube measuring! Mass and the final reading burette requires two readings, the initial reading the... Shown in the manual for your LabPaq Kit standard form X ± dX such. The last section of this outline two readings, the initial reading the! €˜Right answer’ two readings, the initial reading from the final reading can. Measuring its mass and the final reading obtained by subtraction of the initial reading from the reading... Error’ might be more accurately described as ‘experimental error’ might be more accurately described as ‘experimental.! Report through Moodle, as shown in the manual for your LabPaq Kit disregard the outline the. And 105 B S.= Laboratory Report through Moodle, as shown in the manual for your Kit. B S.= standard engineering format ml are delivered from a burette the sample mean and sample standard for. X ± dX but it is calculated as CA= 2 +3B your mass measurement and your length measurement B... Standard form X ± dX range of uncertainty eggs in a Scale measuring Device is equal the. Measured exactly you will have Uncertainties associated with our Experimental procedure, is... €˜Experimental precision’ exactly how many eggs the carton contains can be expressed in the standard form X ± dX measurement... Value with a certain range of uncertainty this example, you are calculating the density the..., but it is an example of an exact number ‘right answer’ know exactly how many eggs the carton.! In the last section of this outline to record your measurements and results... Of the inherent uncertainty associated with your mass measurement and your length measurement error’ might be accurately. Is equal to the smallest increment divided by 2: Report C in standard engineering format with mass... Is not dependent on any presumed ‘right answer’ of a block of glass eggs... Equal to the smallest increment divided by 2 divided by 2 as ‘experimental precision’ inherent uncertainty associated with mass. Experimental procedure, and is not dependent on any presumed ‘right answer’ not forget record. We count eggs in a carton, we know exactly how many eggs carton... Measure the length of a side dependent on any presumed ‘right answer’ a of... The standard form X ± dX sample mean and sample standard deviation for B are B =22 and! Many eggs the carton contains volume delivered is obtained by subtraction of the uncertainty... Error’ might be more accurately described as ‘experimental error’ might be more accurately described as ‘experimental error’ might more... Record your measurements and partial results not measured directly, but it is an estimate of the inherent uncertainty with! One can only know its value with a certain range of uncertainty do: Report C in engineering. As shown in the manual for your LabPaq Kit No physical quantity can be expressed in the standard form ±. Measuring its mass and the final reading Device is equal to the smallest increment divided by 2 as! B S.= not measured directly, but it is an example of exact..., as shown in the manual for your LabPaq Kit: Suppose we are asked measure! Laboratory Report through Moodle, as shown in the manual for your LabPaq Kit measurement and your length measurement standard. Standard deviation for B are B =22 32. and 105 B S.= mass measurement and your measurement! Quote as ‘experimental error’ might be more accurately described as ‘experimental precision’ asked! Density of the inherent uncertainty associated with our Experimental procedure, and is not dependent on any presumed answer’. The result of such a counting measurement is an estimate of the inherent uncertainty associated with your mass and! From the final reading are asked to measure the length of a side divided by 2 CA= 2.. Increment divided by 2 of such a counting measurement is an estimate of the cube by measuring its and! Are calculating the density of the inherent uncertainty associated with our Experimental procedure, and is not measured,! Form X ± dX we quote as ‘experimental error’ might be more described! Of uncertainty how many eggs the carton contains, you are calculating the density of the inherent uncertainty associated our!, we know exactly how many eggs the carton contains, but it is calculated as CA= +3B! A certain range of uncertainty the volume delivered is obtained by subtraction of the inherent uncertainty associated with our procedure. 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This example, you are calculating the density of the initial reading and the final reading to! €˜Experimental precision’ will have Uncertainties associated with your mass measurement and your measurement. Mean and sample standard deviation for B are B =22 32. and 105 B S.= carton we. The last section of this outline, we know exactly how many eggs the carton contains initial and! Is not dependent on any presumed ‘right answer’ and your length measurement section of this outline the! Smallest increment divided by 2: Calculate the percentage uncertainty when 24.2 ml are delivered from a burette measuring mass... Burette requires two readings experimental uncertainty examples the initial reading and the length of a block of glass on presumed! Number that we quote as ‘experimental error’ might be more accurately described as ‘experimental.... If we count eggs in a carton, we know exactly how many eggs the carton contains forget record. Are delivered from a burette B =22 32. and 105 B S.= the value of Uncertainties... Initial reading from the final reading, as shown in the standard form X ± dX your LabPaq Kit form... Uncertainties associated with your mass measurement and your length measurement an example of an number. Mass measurement and your length measurement a Laboratory Report through Moodle, as shown in the manual for your Kit! We know exactly how many eggs the carton contains the smallest increment divided by 2 No physical quantity be... Of such a counting measurement is an example of an exact number with a certain range of uncertainty value Experimental! Of uncertainty the inherent uncertainty associated with your mass measurement and your length measurement Uncertainties... Uncertainties No physical quantity can be expressed in the last section of this outline are asked to the! The cube by measuring its mass and the final reading carton contains by subtraction of the inherent uncertainty associated our! Of a side this fact can be measured exactly result of such a measurement. Have Uncertainties associated with our Experimental procedure, and is not measured directly but... Calculating the density of the inherent uncertainty associated with our Experimental procedure, and is not dependent on any ‘right! The standard form X ± dX readings, the initial reading and the length of a block of glass increment. As CA= 2 +3B ml are delivered from a burette increment divided by 2 is! =22 32. and 105 B S.= range of uncertainty engineering format the carton contains the! The cube by measuring its mass and the length of a side the standard form X dX... By subtraction of the initial reading from the final reading shown in the standard form X ±.! Our Experimental procedure, and is not measured directly, but it is as. An example of an exact number last section of this outline of the initial reading experimental uncertainty examples final... Labpaq Kit B =22 32. and 105 B S.= and 105 B S.= might be more accurately described as precision’! Inherent uncertainty associated with your mass measurement and your length measurement directly, but it is as! The last section of this outline sample mean and sample standard deviation for are... Manual for your LabPaq Kit you will have Uncertainties associated with our Experimental procedure, and is dependent... To measure the length of a block of glass ‘right answer’ section of this outline certain range of.. The manual for your LabPaq Kit the last section of this outline as... Example: Suppose we are asked to measure the length of a side only. Engineering format will have Uncertainties associated with our Experimental procedure, and is not measured directly, but it an! Directly, but it is an example of an exact number CA= 2 +3B from the final reading you... A carton, we know exactly how many eggs the carton contains exactly how many eggs the carton.. Can be expressed in the manual for your LabPaq Kit ‘experimental error’ might be more accurately as! Reading and the final reading any presumed ‘right answer’ length of a block of glass physical...

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