Application of Statistical Concepts in the Determination of Weight Variation in Samples
Bautista, Alyssa Marie F. 1, Elpa, Maxine Sebastianne C. 1
1 Department of Food Science and Nutrition, College of Home Economics
University of the Philippines, Diliman, Quezon City, Philippines
Date Due: 07 Dec 2012
Date Submitted: 07 Dec 2012
Keywords: Experimental errors, Deviations, Statistics, Sampling
At the start of the experiment, twenty (20) pieces of ten-peso coins have been collected. From these, ten (10) were randomly chosen as samples for the experiment. The samples were placed on a clean tissue paper to avoid being tinged with fingerprints. An analytical balance ...view middle of the document...
The watch glass was needed to be emptied because the analytical balance would have reached its weight limit and might post incorrect readings. The process of taring is important to be able to come up with an accurate data. During this process, the equipment’s doors were secured so that no air would interfere it from calibrating back to the zero reading. After all this preparation can the experiment proper be started. During the recording of data, the uncertainty of the equipment used must be accounted. The uncertainty of a particular instrument or equipment shows the extent of which these could commit an error during the actual use. On doing this, the possible errors can be cancelled through the computation stage.
Table I. List of the individual weights of the ten (10) samples
Sample No. | Weight, g |
1 | 5.4320 0.0002 |
2 | 5.4328 0.0002 |
3 | 5.3924 0.0002 |
4 | 6.0733 0.0002 |
5 | 5.4449 0.0002 |
6 | 5.3300 0.0002 |
7 | 5.4088 0.0002 |
8 | 5.4285 0.0002 |
9 | 5.4677 0.0002 |
10 | 5.3837 0.0002 |
Even though a number of procedures had been done to be able to reduce the amount of error propagated, whatever type they may be, several factors which are not observable to the experimenters might have interfere during the weighing process. For this reason, statistical methods were used to quantitatively obtain the apparent weight of the 1-peso coin according to the sample gathered. The results were also tested by their precision from one another. Precision describes the degree of agreement between the measured values.
The initial treatment of results was the Q-test. This is given by the formula,
Qexp= |Xq- Xn|R (1)
where Xq = the questionable result
Xn = the value closest to the questionable result
R = the range of the data set.
This test is used to determine whether the extremities of the set is to be accepted or rejected. The criteria for the acceptance or rejection is based on tabulated values which are unique for a particular number of sample. A data must be rejected if the computed value for the Q-test exceeds the assigned tabulated value. On the other hand, a data is accepted if the value obtained is smaller than that of the tabulated equivalent. The rejected data would no longer be included on the computation of the measurements of precision and central tendency.
For Data Set 1, the values which have been tested using the method are: H: 6.7033 0.0002 g and L: 5.3300 0.0002 g. These were verified under the 95% certainty level. The higher extremity, 6.0733 0.0002 g, has been rejected because the Qexp was equal to 0.845, exceeding the tabulated value of 0.625 for a data set of six (6) samples. The other value has been accepted because the Qexp for this data equals 0.0839 which was far less than the tabulated value of 0.625. For Data Set 2, the same values were tested, and still, 6.0733 0.0002 was rejected for resulting to a Qexp value of 0.815 which exceeds the tabulated value...