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Relative Standard Deviation Standard deviation (stdev) is the usual way of quantifying precision. Calculators with a statistics mode will find the stdev, but in this class, where data sets are typically sm all, an approximation based on the range of the data is ade quate. The range is the difference between the largest and the smal lest in a series of measurements: range = largest smallest. An estimate of the standard deviation is stdev range/p where is taken from the following table. Number of measurements 2 3 4 5 6 8 10 p 1.4 1.9 2.2 2.5 2.7 3.0 3.2 The relative standard deviation (RSD) gives the precision as a percentage of the mean (average). More precise dat a yield a smaller RSD. 100% mean stdev RSD The RSD should be written with 2 significant figure s. Relative Error Relative error is the percent deviation of your val ue from the true or accepted value. Relative error is positive if your value is high and negative if your value is low. I t should also be reported with 2 significant figures. 100% value accepted value accepted value your error Examples A density measurement of solid aluminum was made 3 times. The results were 2.60 g/mL, 2.54 g/mL, 2.70 g/mL. The accepted density for aluminum is 2.70 g /mL. mean = 2.61 g/mL range = 2.70 g/mL 2.54 g/mL = 0.16 g/mL stdev. 0.16 g/mL /1.9 = 0.084 g/mL RSD = 2.3 or 032 .0 mL /g 61.2 mL /g 084 .0 3.3- 100 70 70.2- 61.2 %error Here is another example with less-precise data: 1.45 g/mL, 1.20 g/mL, 1.40 g/mL, 1.60 g/mL, 1.30 g/ mL mean = 1.39 g/mL range = 0.40 g/mL stdev . 0.40 g/mL/2.5 = 0.16 g/mL RSD = 0.12 or 12% No accepted value is given, so % error cannot be calculated.

Calculators with a statistics mode will find the stdev but in this class where data sets are typically sm all an approximation based on the range of the data is ade quate The range is the difference between the largest and the smal lest in a series ID: 22207

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Relative Standard Deviation Standard deviation (stdev) is the usual way of quantifying precision. Calculators with a statistics mode will find the stdev, but in this class, where data sets are typically sm all, an approximation based on the range of the data is ade quate. The range is the difference between the largest and the smal lest in a series of measurements: range = largest smallest. An estimate of the standard deviation is stdev range/p where is taken from the following table. Number of measurements 2 3 4 5 6 8 10 p 1.4 1.9 2.2 2.5 2.7 3.0 3.2 The relative standard deviation (RSD) gives the precision as a percentage of the mean (average). More precise dat a yield a smaller RSD. 100% mean stdev RSD The RSD should be written with 2 significant figure s. Relative Error Relative error is the percent deviation of your val ue from the true or accepted value. Relative error is positive if your value is high and negative if your value is low. I t should also be reported with 2 significant figures. 100% value accepted value accepted value your error Examples A density measurement of solid aluminum was made 3 times. The results were 2.60 g/mL, 2.54 g/mL, 2.70 g/mL. The accepted density for aluminum is 2.70 g /mL. mean = 2.61 g/mL range = 2.70 g/mL 2.54 g/mL = 0.16 g/mL stdev. 0.16 g/mL /1.9 = 0.084 g/mL RSD = 2.3 or 032 .0 mL /g 61.2 mL /g 084 .0 3.3- 100 70 70.2- 61.2 %error Here is another example with less-precise data: 1.45 g/mL, 1.20 g/mL, 1.40 g/mL, 1.60 g/mL, 1.30 g/ mL mean = 1.39 g/mL range = 0.40 g/mL stdev . 0.40 g/mL/2.5 = 0.16 g/mL RSD = 0.12 or 12% No accepted value is given, so % error cannot be calculated.

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