Application of Statistical Concepts in the Weight Variation of Samples

Application of Statistical Concepts in the Weight Variation of Samples

Gliezl Allison G. Imperial

Teshia Faye T. Josue

Institute of Chemistry, College of Science, University of the Philippines, Diliman, Quezon City 1101 Philippines

Department of Chemistry, College of Science, University of the Philippines, Diliman, Quezon City 1101 Philippines

Experimental Detail

The 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.

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 Results

Slight 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 formula

Qexperimental=Qexp= | Xq - Xn |

R

When Qtab<Qexp, the Qexp value calculated is rejected. However when Qtab>Qexp, the Qexp value calculated is accepted. Below is a table showing the calculated Qexp values which are lesser than the Qtab value at 95% confidence level of 0.625 and 0.468 for data set 1 and 2, respectively.

Table 1. Qexp vs. Qtab

Data Set

Suspect Values

Qexp

Qtab

Conclusion

1

3.6410

0.17

0.625

Accepted

3.5793

0.41

2

3.6410

0.17

0.468

Accepted

3.5793

0.41

The 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 formula

Below 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.

Parameter

Data set 1

Data set 2

Mean

3.61 g

3.61 g

Standard Deviation

0.021583 g

0.019017 g

Relative Standard Deviation

0.60%

0.53%

Range

0.0617

0.0617

Relative Range

1.71%

1.71%