Application of Statistical Concepts in the Determination of Weight Variation in Samples
Galingana, Cara Lois T.
Department of Food Science and Nutrition, College of Home Economics University of the Philippines, Diliman, Quezon City
Date Due: December 7, 2012
Date Submitted: December 7, 2012
Keywords: Sampling, Central Tendency, Accuracy, Precision, Quantity, Statistical Tests
RESULTS AND DISCUSSION
In the experiment, the class was able to use an analytical balance properly, gain an understanding of some concepts of statistical analysis, and apply statistical concepts in analytical chemistry.
The data was gathered using an electronic analytical balance. This equipment has a precision and accuracy that exceeds 1 part in 106 at full capacity. It can measure from 0.0001 mg to 30 g. The electronic analytical balance used in the lab features a taring control that disregards the weight of the container on the pan. Thus, the value displayed on the balance only refers to the sample in the container.
Ten 1-peso coins were then collected as samples. Each coin was weighed on the balance, showing variation in the data gathered.
Table 1.1 Weights of Ten 1-Peso Coins Measured on the Electronic Analytical Balance Sample No.
| Weight, g
| 5.3604 ± 0.0002
| 5.4112 ± 0.0000
| Data Set 1
Data Set 1
6.1109 ± 0.0001
| 5.3679 ± 0.0000
| Data Set 2
Data Set 2
5.4044 ± 0.0002
| 5.4066 ± 0.0000
| 5.3139 ± 0.0001
| 6.0423 ± 0.0000
| 5.3742 ± 0.0002
| 5.4798 ± 0.0001
The first 6 samples were grouped as Data Set 1, while all 10 samples were grouped as Data Set 2. These data sets were then used for statistical analysis.
The first statistical test done in the experiment is the mean. This test is a measure of central tendency, which is used as the average with interval or ratio data. It is considered to be the center of gravity of distribution, because the sum of the distances of the measures from the mean on one side is equal to the sum of the distances on the other side (Downie, 1983).
Where Xi represents the individual values of X making up a set of n replicate measurements (Institute of Chemistry, 2012).
Standard deviation, a measure of precision, was then calculated using the computed value from the average weights of each data set. The standard deviation indicates the extent of randomness of individuals about their common average (Siegel, 1994).
On the other hand, the relative standard deviation presents the precision of the data clearer than the standard, because its relation to the mean in parts per thousand is shown.
RSD= sX x 1000 ppt
Table 1.2 Computed Values for the Mean, Standard Deviation and Relative Standard Deviation of Data Sets 1 and 2 Parameter
| Data Set 1
| Data Set 2
| 5.5102 ± 0.00005
| 5.5272 ± 0.00004
Rel. S. Dev.
Another measure of precision was done in this experiment, the range. It is simply the difference between the highest and the lowest value in a data set. This is the least reliable of the measures, but it may be used with ordinal, interval or ratio data (Downie, 1983).
R = Xhighest - Xlowest
However, the relative range, same as the relative standard deviation, is much preferred by researchers, because of its more visual form. The relationship of the range to the mean is then shown.
RR= RX x 1000 ppt
To establish an interval surrounding an experimentally determined mean within which the population mean is expected to lie with a certain degree of probability, the confidence limits are computed (Skoog, 2010). The statistical test was set at 95% confidence level, which implies the possibility that the true value lies within the range.
The confidence interval was computed as the mean ± the values for t for...
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