Application of Statistical Concepts in the Determination of Weight Variation in Samples 1
Lope Immanuell C. Santos IV , (Jayrald Calixtro)
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Department of Mining, Metallurgical, Metallurgical, and Materials Materials Engineering, Engineering, College College of Engineering Engineering Department of Chemical Chemical Engineering, Engineering, College College of Engineering Engineering University of the Philippines, Diliman, Quezon City, Philippines Date Due: June June 28, 2013 2013 Date Submitted: Submitted: June 28, 2013 2
Abstract
This experiment aims to properly measure data and use statistical parameters in order to determine whether a set of values should be accepted or not, and also to determine its deviation from the true value. Ten pieces of one-peso coins were placed in a 50-mL beaker and was measured inside an analytical balance. Each coin was then removed removed one by one measuring the difference of each measurement measurement to determine the weight of the removed coin. This was done until all coins were removed from the beaker. There has been a small value of uncertainty due to the small uncertainty of the analytical balance, 0.0002. From the Q-Test, it can be deduced that both Data Set 1 and 2 have accepted values, from the Q tab and Qexp.
INTRODUCTION
Analytical Chemistry will be dealing about more about the quantity of each measurement rather than its quality. This is where statistical parameters parameters take into place to be used as tools to determine whether a set of data is reliable enough or not.
∑ Relative standard deviation is another parameter used. It can be computed by the formula:
There are a number of statistical parameters that were used in this experiment.
Range can be defined as the difference between the maximum and the minimum values of a given population.
Q-Test was performed to determine whether the values obtained are to be accepted or rejected from their tabular and experimental values of Q.
First, the mean, or the average of the population. The mean can be solved by:
∑
Another statistical parameter that was used in the experiment was standard deviation (s). This can be computed by the formula:
Relative Range was also one of the parameters used in this experiment. It can be computed as:
The last parameter used in the experiment was the confidence limits. It can be computed as: [1]
√
Data Set 2 was then composed of all the samples (10). These include the 6 coins from Data Set 1. These weights show as follows:
METHODOLOGY
Ten samples, one-peso coins, were prepared for weighing. Each has been cleaned by a lint free tissue paper to ensure that only the mass of the coin would be measured, removing the materials that are in the surface of the coin. All samples were then placed inside a 50-mL beaker, then placed inside the analytical balance. The reading was then recorded to the lab notebook. Each coin was then removed from the analytical balance, one by one, as each change in the weight will determine the weight of the coin removed. This has been done until all coins have been removed and the only thing left inside the analytical balance is the 50-mL itself. RESULTS AND DISCUSSION
During the experiment, the proper use of the analytical has been observed. It is also noted that the uncertainty of this balance is 0.0002. Statistical concepts has also been used throughout the experiment to determine whether the results have a relevance or not. Each weight then obtained by getting the difference of 2 consecutive reading from the analytical balance. Two Data Sets has also been imposed to the samples for further statistical analysis. Data Set 1 composed of the first 6 coins removed from the analytical balance. These weights show as follows: Table 1. Data Set 1. Sample No. 1 2 3 4 5 6
Weight (in grams) 5.4482 ± 0.0003 5.4604 ± 0.0003 5.5296 ± 0.0003 5.4226 ± 0.0003 5.4266 ± 0.0003 5.4008 ± 0.0003
Table 2. Data Set 2. Sample No. 1 2 3 4 5 6 7 8 9 10
Weight (in grams) 5.4482 ± 0.0003 5.4604 ± 0.0003 5.5296 ± 0.0003 5.4226 ± 0.0003 5.4266 ± 0.0003 5.4008 ± 0.0003 5.4706 ± 0.0003 5.3889 ± 0.0003 5.3095 ± 0.0003 5.4245 ± 0.0003
Q-Test was also performed to the population. This needs to be performed to determine whether a set of data of an experiment should be accepted or rejected, depending on their Q tab and Qexp[2]. The following table is the performed Q-Test over the population of this experiment. Table 3. Q-Test. Data Suspect Set Values 1 H: 5.5296 L: 5.4008 2 H: 5.5296 L: 5.3095
Qtab
Qexp
Conclu sion
0.625 0.625 0.466 0.466
0.537 0.169 0.268 0.361
Accepted Accepted Accepted Accepted
Note: H – highest suspect value, L – lowest suspect value
The table above means all values of the experiments are considered to be accepted. This could mean a small deviation between variables. The following statistical parameters were also computed for this experiment: mean, standard deviation (S), relative standard deviation (in ppt) (RSD), range (R), relative range (in ppt) (RR), and confidence limits (95%). Table 4. Statistical Parameters for Data Set 1.
Table 5. Statistical Parameters for Data Set 2. Parameter X S RSD R RR CL
5.4282 ± 0.0009 0.06 10 0.2201 ± 0.0004 40.55 ± 0.08 5.4282 ± 0.0412
The above tables show the different values of different statistical parameters for Data Sets 1 and 2. The statistical parameters from Data Set 1 have smaller values of uncertainty than Data Set 2 since Data Set 2 has more samples taken into account, therefore having a higher uncertainty value. The mean, as we all know, is the central value of a set of values. It is computed by dividing the sum of all values by the number of samples. The standard deviation is computed as the square root of the summation of the difference of each variable to the mean divided by the number of samples, minus one. The standard deviation can also give an approximation of how far are the obtained values from the central value, or the mean. [3] The confidence level is a range of values wherein you know, somewhere within that value, the true value exists. It can be estimated to be almost near from the average of the population involved. One thing also observed during the run of the experiment is that you can only touch the samples using a forcep or crucible tong. It is to prevent bacteria or any other foreign object to be in contact with the samples inside the analytical balance since the balance is very sensitive and can measure up to 0.0001 of a gram. In every experiment, errors are always present. There are three types of errors: random, systematic, and human. Random errors are errors that naturally exist in all experiments. One example of this is the measuring device used was not really 100% precise of its measurement.
Parameter X 5.4480 ± 0.0007 S 0.05 RSD 10 R 0.1288 ± 0.0004 RR 23.64 ± 0.08 CL 5.4480 ± 0.0473 Systematic errors are errors that are caused by the methods used during the experiment. One possible example of a systematic error in the experiment is if the analytical balance is not yet set to zero when you put the 50-mL beaker with the samples inside. Human errors are errors that are due to human activity. If this has been an error in an experiment, the experiment must be redone since it would already have a high level of uncertainty due to this error. CONCLUSION
Based on the statistical parameters, it can be therefore concluded that the values obtained can be considered accepted due to the result of the Q-test. There has also been only a small amount of uncertainty throughout the experiment since the analytical balance is precise enough to lower the values of the uncertainties. This experiment could have been done better if the platform wherein the analytical balance is placed would be shock proof so that it would be less sensitive about extraneous nuisances. REFERENCES
[1] Skoog, et al., Fundamentals of Analytical Chemistry, Eighth edition, 2004, [2] Institute of Chemistry, UP Diliman. (2007). Analytical Chemistry Laboratory Manual, Institute of Chemistry. UP Diliman. pp 8-11. [3] Coolidge, Statistics; A Gentle Introduction, Third Edition, 2013, p 89.
