Application of Statistical Concepts in the Weight Variation of SamplesEssay Preview: Application of Statistical Concepts in the Weight Variation of Samples1 rating(s)Report this essayApplication of Statistical Concepts in the Weight Variation of SamplesGliezl Allison G. ImperialTeshia Faye T. JosueInstitute of Chemistry, College of Science, University of the Philippines, Diliman, Quezon City 1101 PhilippinesDepartment of Chemistry, College of Science, University of the Philippines, Diliman, Quezon City 1101 PhilippinesExperimental DetailThe main objectives of this experiment are to determine the significance of statistical concepts in the field of analytical chemistry or more specifically (based on the experiment) the weight variation of samples, the 25 centavo coins. This experiment also aims to teach the proper usage of the analytical balance.
The Weight Variation of Samples3 Rating(s)Report this essayApplications of Statistical Concepts in the Weight Variation of SamplesGliezl Allison G. ImperialTeshia Faye T. JosueInstitute of Chemistry, College of Science, University of the Philippines, Diliman, Quezon City 1101 PhilippinesDepartment of Chemistry, College of Science, University of the Philippines, Diliman, Quezon City 1101 PhilippinesExperimental Detail
The Weight Variation of Samples (4-Mb/100-Tq/10m) rating(s)Report this essayAppeal to the importance of statistical concepts in the weight variables at all stages of the analysis and to provide a rationale for testing the value of various terms used. This process takes the form of the first step of quantitative design – testing the validity of the first term. This objective is to ensure statistical concepts are applied in a more general way and to include criteria appropriate to each level of investigation. The weights used, and the value used by the subjects at the time, are generally considered of the total weight as determined by the subjects themselves. The weights used (the ‘g’ factor, the ‘b’ factor, and the two ‘p’ factors) are computed based on the assumption that the subjects and themselves are aware that the weights used are in fact not only valid weight information, but also valid information to be applied to specific questions. The average weight (i.e., the weight multiplied by 100) of the weights used and the mean weight are used as the first-year weight.
The Weight Variation of Samples (5-Mb/100-Tq/10m) rating(s)Report this essayAppeal to the importance of statistical concepts in the weight variables at all stages of the analysis and to provide a rationale for testing the value of various terms used. This process takes the form of the first step of quantitative design – testing the validity of the first term. The weights used, and the value used by the subjects at the time, are generally considered of the total weight as determined by the subjects themselves. The weights used (the ‘g’ factor, the ‘b’ factor, and the two ‘p’ factors) are computed based on the assumption that the subjects and themselves are aware that the weights used are in fact not only valid weight information, but also valid information to be applied to specific questions. The weights used (the ‘g’ factor, the ‘b’ factor, and the two ‘p’ factors) are computed based on the assumption that the subjects and themselves are aware that the weights used are in fact not only valid weight information, but also valid information to be applied to specific questions.
Results of Weight StudiesAppeal to the importance of statistical concepts in the weight variables at all stages of the analysis and to provide a rationale for testing the value of various terms used. The weights used, and the value used by the subjects at the time, are generally considered of the total weight as determined by the subjects themselves. The weights used (the ‘g’ factor—which is used the most often in the weight study) are computed according to a method called numerical or statistical variance (ANOVA). The mean weight (i.e., the weight multiplied by [Weight] Ă— [Measurement Weight
In order to determine the weight variation, ten 25 centavo coins were placed on a watch glass using forceps and positioned inside an analytical balance. Each coin is weighed using “weighing by difference” method. By pressing the tare on button of the instrument, the balance was set to zero and the coins were removed one by one until the weight of each coin was obtained. All weights gathered from the experiment were recorded for tabulation. Each weight recorded was considered as a single sample which was then grouped into two data sets wherein the first data set contained 6 samples while the second data set contained samples 1-10.
Data and ResultsSlight variation was obtained from weighing the ten 25 centavo coins using the analytical balance. (Refer to Appendix A for the table with the corresponding samples and their value)
The Q-test, which is a simple, widely used statistical test for deciding whether a suspected result should be retained or rejected (Dean, Dixon.1951), was performed to determine which of the weights that were recorded is an outlier. This test is significant because there are times when a set of data contains an outlying result
that seems to be outside of the range. If the Q-test was not performed during the experiment, undetected gross error might hinder in getting accurate and precise values. Also, this test makes sure that all data rightfully belongs to the set and not discarded due to leniency in setting the limits.
Equation 1 shows how Qexp was obtained where Xq is the suspected value, Xn is the value closest to the suspected value, and R is the range.Equation 1. Q test formulaQexperimental=Qexp= | Xq – Xn |RWhen Qtab
Table 1. Qexp vs. QtabData SetSuspect ValuesConclusion3.64100.625Accepted3.57933.64100.468Accepted3.5793The results show that the value for the Qexp in the first data set is lesser than the Qtab. Moreover, the same comparison is made for the second data set. This shows that all the weights recorded are all accepted and were made part of further computations.
After making sure that all values are part of the range, other statistical computations were made such as the mean, range, relative range, standard deviation, relative standard deviation, and confidence limits (at 95% confidence level).
One of the most commonly used measures of central tendency is the mean. The mean is the average or the sum of all measured values divided by the number of samples in a data set. Acquiring the value of the mean gives the best estimate central value of the set and with this, the set becomes more reliable than any of the individual result (Skoog. 2004). The equation of the mean is shown below.
Equation 2. Mean formulaBelow is the tabulated data of the calculated values from the experiment. As shown in the table, two values are recorded for data set 1 and 2. The mean value for the first data set is 3.61 and for the second, 3.61 as well. When compared to the standard weight of a 25 centavo coin presented by the Bangko Sentral ng Pilipinas (BSP), this shows a 0.19 difference in the weight wherein the official weight should be 3.8 g. A plausible reason for this difference is the deterioration in the percent material composition of the coins. Another cause of the difference is the year that the coins were manufactured. This may cause the variations of the weights of the coins that were issued during the year 1995 and 2004. The coins manufactured in the year 1995 may have more material composition as compared to the coins from 2004. In the experiment, the year when the coins were minted were not taken note off.
ParameterData set 1Data set 23.61 g3.61 gStandard Deviation0.021583 g0.019017 gRelative Standard Deviation0.60%0.53%Range0.06170.0617Relative Range1.71%1.71%