Application of Statistical Concepts in the Determination of Weight Variation in Samples

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Application of statistical concepts in the determination of weight variation in samples

G.E.
Institute of Biology, College of Science
University of the Philippines, Diliman, Quezon City, Philippines Date Submitted: April 23, 2013

ABSTRACT
Statistics is a mathematical science dealing with the collection, organization, analysis, interpretation, and presentation of data. It provides a more accurate way of expressing data rather than mere observation. This experiment used the different statistical concepts such as the Q test, mean, standard deviation, relative standard deviation, range, relative range, and confidence limits or confidence intervals. The results generated from these tests are used as a basis to check whether the values obtained from weighing 10, 25 centavo coins using an analytical balance and which were grouped into two data sets, are acceptable or not. It can be seen that when the statistical concepts were applied to data set 1 and data set 2, the resulting values obtained do not greatly vary. However, it can’t be proven that the results do not differ significantly since there was no test performed to check this.

RESULTS AND DISCUSSION
Different weights were obtained from the 10- 25 centavo coins using the analytical balance. Each weight is considered as a single sample. The samples were grouped into two data sets. The first dataset contains six samples while the second data set contains 10 samples. The table below shows the two data sets with their corresponding samples. Table 1. Weight of samples grouped into two sets

DATA SET 1 (g)| DATA SET 2 (g)|
3.5348| 3.5348|
3.556| 3.556|
3.5806| 3.5875|
3.5902| 3.5806|
3.6113| 3.5851|
3.6484| 3.5875|
 | 3.5902|
| 3.6113|
| 3.624|
| 3.6484|

The Q test was performed for each of the data sets. Other statistical parameters were also calculated. When one or more of the measured values obtained within a set is/are different from the rest, the Q test can be used to check if the suspected value or values should be retained or rejected (chem.uoa.gr). However this is only used for a small number of samples or replicates in a given set. Hence, this test is used in this experiment. Furthermore, the Q test is an example of a significance test. The outcome of this test is the acceptance or the rejection of the null hypothesis. For the purpose of this paper, the null hypothesis would be that, there is no significant difference between the suspected value or values from that of the rest of the values obtained. 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 formula

When Qtab<Qexp, the calculated Qexp value is rejected. However when Qtab>Qexp, the calculated Qexp value is accepted. The results shown in the table below shows that the calculated Qexp values are less than their corresponding Qtab values at 95% confidence level. Hence, these values are accepted. This also means that there is no significant difference between the suspected values from that of the rest of the values obtained. Furthermore, any discrepancies or differences are due to purely random and not systematic errors. Table 2. Obtained Qexp versus Qtab

Data Set| Suspect Values| Qtab| Qexp| Conclusion|
1| H: 3.6484 g| 0.625| 0.3266| ACCEPT|
| L: 3.5348 g| 0.625| 0.1866| ACCEPT|
2| H: 3.6484 g| 0.466| 0.2148| ACCEPT|
| L: 3.5348 g| 0.466| 0.1866| ACCEPT|

To discuss further, random errors are errors that are due to unknown or unpredictable changes in the experiment (physics.umd.edu). These errors are beyond the control of the person taking the measurement. On the other hand, systematic errors are errors that usually come from the instruments used in taking the measurement (citycollegiate.com). As mentioned, other statistical parameters were also calculated. These include the mean, standard deviation,...
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