Standard Deviation, Confidence Limit and O
Abstract:
According to the different statistical tools it was possible to define that in laboratory the volume of 1 drop is 0.026054 ml, it was concluded that the calculations are representative because the propagation of errors for calculation of volume of 1 drop is 0.005482 ml. Finally, the number of moles and number of drops of H_{2}O needed to have 0.5 atm vapor pressure in 1 liter. 11.48022 drops and 0.016347 moles
Introduction:
All experimental measurements are affected by an inherent imprecision in the measurement process. Since this is basically a matter of comparing with a standard and this comparison is made with an apparatus, the measurement will depend on the minimum quantity that it is able to measure. And this amount is decreasing with the progress of physics in a continuous process, but with no apparent end. That is, although each time we can give the measure with more “decimals”, the next “decimal” will not be known.
Procedure and Results:
 Table 1
Table 1  
Trial  V, ml  DV, ml  m, g  Dm, g 
1  1  1  26.6384  0.8097 
2  1.6  0.6  27.3222  0.6838 
3  2.1  0.5  27.9214  0.5992 
4  3  0.9  28.657  0.7356 
5  3.8  0.8  29.4867  0.8297 
6  4.4  0.6  30.2572  0.7705 
7  5.2  0.8  30.9415  0.6843 
8  6  0.8  31.6862  0.7447 
9  6.8  0.8  32.5244  0.8382 
 Qtest for all experimental data.
Q tests  
Trial  DV  Dm 
1  0.103448  0.116174 
2  0.086207  0.101801 
3  0.086207  0.101801 
4  0.137931  0.124975 
5  0.103448  0.130904 
6  0.103448  0.116259 
7  0.137931  0.116259 
8  0.137931  0.142406 
9  0.137931  0.142406 
 Standard deviations, standard errors of mean and C.L. for volume and mass:
Table 2
DV, ml  Dm, g  
Mean  0.755556  0.743967 
Std dev, S_{x}  0.15899  0.078631 
Error of mean, d_{x}  0.052997  0.02621 
C.L.  0.122422  0.060546 
 Mean density of watercalculated using mean volume from cylinder readings and mean masses from analytical balance measurements.984662 g/ml
 Propagation of errors for density calculations above.231868 g/ml
 Plot (m vs V) and Linest (Excel) data.
LINEST data


1.004782  25.7081 
0.013518  0.057007 
0.998735  0.0769 
5524.627  7 
32.67025  0.041395 
 Tabulate results:
Table 3
r ± C.L. (from mean Dm and DV), g/ml  r ± C.L. (from plot), g/ml 
(9.85± 2.32) * 10^{1}  1.00± 0.01 
 You should round off the reported values. How many digits should you report in final answer for analytical balance? Points will be taken off for incorrect rounding.
 The order of magnitude of the result should be as clear as possible. Therefore, the preferred notation of for instance 0174 ± 0.0002 is (1.74 ± 0.02)·10^{2}.
 Volume of 1 drop.026054 ml
 Propagation of errors for calculation of volume of 1 drop.005482 ml
 Number of moles and number of drops of H_{2}O needed to have 0.5 atm vapor pressure in 1 liter.48022 drops and 0.016347 moles
(This data will be needed for your future experiments)
Discussion:
Different variations in laboratory measurements can be found due to the errors listed below.
Instrumental errors (of apparatus): for example, the calibration error of the instruments.
– Personal error: This is, in general, difficult to determine and is due to personal limitations. Like, for example, parallax errors, or visual problems.
– Measurement method errors, which correspond to an inappropriate choice of the measurement method; This includes three different possibilities: the inadequacy of the measuring device, the observer, or the measurement method itself.
Statistical tools allow from a database, to define the its trend based on other variables. However, the purpose is to find a trend that perfectly describes the phenomenon. Therefore, with a defined trend and an explained phenomenon, measurements can be ruled out as incorrect.Also in the case of having many measurements, the value that is most representative of the group studied could be defined.
References:
https://en.wikipedia.org/wiki/Standard_error
https://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm
https://www.itl.nist.gov/div898/handbook/mpc/section5/mpc55.htm
https://en.wikipedia.org/wiki/Propagation_of_uncertainty
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