# Experiment 1 Application of Statistical Concepts in the Determination of Weight Variation in Samples

**Topics:**Statistics, Sample size, Normal distribution

**Pages:**8 (2315 words)

**Published:**November 22, 2012

Chem 26.1 WFV/WFQR1

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Nov. 23, 2012

A skillful researcher aims to end his study with a precise and accurate result. Precision refers to the closeness of the values when some quantity is measured several times; while accuracy refers to the closeness of the values to the true value. The tool he utilizes to prevent errors in precision and accuracy is called statistics. In order to become familiar to this tactic, the experiment aims to help the researchers become used to the concepts of statistical analysis by accurately measuring the weights of ten (10) Philippine 25-centavo coins using the analytical balance, via the “weighing by difference” method. Then, the obtained data divided into two groups and are manipulated to give statistical significance, by performing the Dixon’s Q-test, and solving for the mean, standard deviation, relative standard deviation, range, relative range, and confidence limit—all at 95% confidence level. Finally, the results are analyzed between the two data sets in order to determine the reliability and use of each statistical function.

RESULTS AND DISCUSSION

This simple experiment only involved the weighing of ten 25-centavo coins that are circulating at the time of the experiment. In order to practice calculating for and validating accuracy and precision of the results, the coins were chosen randomly and without any restrictions. This would give a random set of data which would be useful, as a statistical data is best given in a case with multiple random samples. Following the directions in the Analytical Chemistry Laboratory Manual, the coins were placed on a watch glass, using forceps to ensure stability. Each was weighed according to the “weighing by difference” method. The weighing by difference method is used when a series of samples of similar size are weighed altogether, and is recommended when the sample needed should be protected from unnecessary atmosphere exposure, such as in the case of hygroscopic materials. Also, it is used to minimize the chance of having a systematic error, which is a constant error applied to the true weight of the object by some problems with the weighing equipment. The technique is performed with a container with the sample, in this experiment a watch glass with the coins, and a tared balance, in this case an analytical balance. The procedure is simple: place the watch glass and the coins inside the analytical balance, press ON TARE to re-zero the display, take the watch glass out, remove a coin, then put the remaining coins back in along with the watch glass. Then, the balance should give a negative reading, which is subtracted from the original 0.0000g (TARED) to give the weight of the last coin. The procedure is repeated until the weights of all the coins are measured and recorded. The weights of the coins are presented in table 1, as these raw data are vital in presenting the results of this experiment. Table 1. Weights of 25-centavo coins measured using the “weighing by difference” method| Sample No.| Weight, g|

1| 3.6072| Data Set 2| Data Set 1|

2| 3.7549| | |

3| 3.6002| | |

4| 3.5881| | |

5| 3.5944| | |

6| 3.5574| | |

7| 3.5669| |

8| 3.5919| |

9| 3.5759| |

10| 3.6485| |

Note that the data are classified into two groups, Data Set 1 which includes samples numbered 1~6 and Data Set 2 which includes samples numbered 1~10. Since the number of samples is limited to 10, the Dixon’s Q-test was performed at 95% confidence level in order to look for outliers in each data set. The decision to use the Q-test despite the fact that there were only a few, limited number of samples and to use the confidence level of 95% was carried out as specified in the Laboratory Manual. Significance of Q-test

The Dixon’s Q-test aims to identify and...

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