4. In an experiment, you get the following data to determine the density )15.472
ID: 1074697 • Letter: 4
Question
4. In an experiment, you get the following data to determine the density )15.472 Volume(mL)19.63 Trial Mass(g) 2 17.575 22.25 14.675 18.60 4 17.645 22.35 19.090 20.38 (1) Calculate the mean of the density, the average deviation, the variance, the estimated standard deviation, the estimated standard deviation of the mean and the range of the results. (2) If the uncertainty in the measurement of mass is 0.001 g and the uncertainty in the measurement of volume is 0.05 mL, Find the uncertainty in densityExplanation / Answer
(1) The average density = (0.7882 + 0.7899 + 0.7900 + 0.7895 + 0.9367)/5 = 0.81886
The standard deviation (s) = [{(0.7882-0.81886)2 + (0.7889-0.81886)2 + (0.7900-0.81886)2 + (0.7895-0.81886)2 + (0.9367-0.81886)2}/(5-1)]1/2 = 0.06588
The variance (s2) = (0.06588)2 = 0.00434
The estimated standard deviation () = [{(0.7882-0.81886)2 + (0.7889-0.81886)2 + (0.7900-0.81886)2 + (0.7895-0.81886)2 + (0.9367-0.81886)2}/5]1/2 = 0.05892
The estimated standard deviation of the mean = /51/2 = 0.05892/51/2 = 0.02635
The range of density results = 0.9367 - 0.7882 = 0.1485
(2) The uncertainity in density = uncertainity in mass/uncertainity in volume = 0.001 g/0.05 mL = 0.02 g/mL
Trial 1 2 3 4 5 Density 15.472/19.63 = 0.7882 17.575/22.25 = 0.7899 14.675/18.60 = 0.7900 17.645/22.35 = 0.7895 19.090/20.38 = 0.9367Related Questions
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