# APPLICATION OF STATISTICAL CONCEPTS IN THE DETERMINATION OF WEIGHT VARIATION IN SAMPLES

M.C. MENDOZA1

1NATIONAL INSTITUTE OF MOLECULAR BIOLOGY & BIOTECHNOLOGY, COLLEGE OF SCIENCE UNIVERSITY OF THE PHILIPPINES, DILIMAN, QUEZON CITY 1101, PHILIPPINES DATE SUBMITTED: 21 NOVEMBER 2013

DATE PERFORMED: 14 NOVEMBER 2013

ABSTRACT

Accuracy and precision are critical concepts to the performance of a laboratory to produce sound analytical results (Singer, 2001). LOLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL

RESULTS AND DISCUSSION

The analytical balance was used in this experiment to determine the weight of each 25 centavo coin. This was done by performing the weighing by difference method. Results were then recorded in table 1. Table 1 below shows the weight of the ten samples of coins. The samples were then divided into two data sets; samples 1-6 (data set 1) and samples 1-10 (data set 2).

Table 1.Weight of 25 centavo coin samples

Sample No.

Weight, g

1

3.5800

Data Set 2

Data Set 1

2

3.6073

3

3.5904

4

3.6140

5

3.5940

6

3.6265

7

3.6016

8

3.7603

9

3.5974

10

3.5978

Since this experiment aims to apply some statistical concepts in analytical chemistry, statistical tests were done in order to assess both precision and accuracy of the data gathered.

However in an experiment, it is possible that some of the data gathered can be considered invalid. These outliers are usually the highest or the lowest value in a set of data which differ significantly from the other observations. In presence of which, some statistics, like the mean, are greatly affected especially if there is a small number of observations. Hence, for this experiment to have accurate and precise conclusions, a test for detecting outliers must first be performed before proceeding with the analysis. The Dixon’s Q-test is one of the most commonly used test where in Qexperimental (1) is calculated and compared with Qtabulated, the tabulated Q-value at a certain confidence level.

Qexp=

Xq is the questionable value,Xn is the measurement numerically closest to theXq, and R is the range of the data set obtained from subtracting the lowest value from the highest value in a set of measurements.

To eliminate the data outside the normal distribution, Q-test was performed. Table 2 shows that at 95 % confidence level,Qtab for Data Set 1 is 0.625 while Qtab for Data Set 2 is 0.466. Qexpfor both data sets (extreme values) were calculated and compared with respective Qtabvalues. In such cases like the suspected value of 3.7603 grams in Data Set 2 wherein calculated Qexpis greater than Qtab, decision is to reject the suspected value.Therefore at 95% confidence level, this value is concluded to be an outlier whereas the other suspected values (3.6265 g, 3.5800 g, and 3.5798 g) are not.

Table 2.Determination of Outliers in Data Sets 1 and 2

Data Set

SuspectedValues

Qtab

Qexp

Conclusion

1

H: 3.6265

0.625

0.2688

NOT AN OUTLIER

L: 3.5800

0.625

0.2237

NOT AN OUTLIER

2

H: 3.7603

0.466

0.7413

OUTLIER

L: 3.5798

0.466

0.0011

NOT AN OUTLIER

As Sample No. 8 was eliminated from the observations to be used in the computations( in Data Set 2), data sets were then subjected to Measures of Central Tendency, Measures of Precision, as well as confidence limit.

According to Sirug (2011), a measure of central tendency is a single value that can represent a collection of observations and one of the most common types of this measure is the mean. The sample mean can be an estimator of the population mean. He also noted the mean is the only measure in which all observations in a data set play an equal role in determining its value. Having the outlier rejected in this experiment, the mean can now be a good measure of central tendency. Equation of the mean(2) is shown below.

x̄

Table 3 below shows the calculated values from the experiment. The mean values...

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