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

**Topics:**Normal distribution, Measurement, Statistics

**Pages:**8 (1481 words)

**Published:**December 23, 2012

del Castillo, Kevin S.

Department of Food Science and Nutrition, College of Home Economics University of the Philippines, Diliman, Quezon City, Philippines Date: 26 November 2012

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Results and Discussion

Statistics is one of the important tools used in chemistry. It defines the measurements gathered, and characterizes the relationship of each value to each other. The experiment aimed to use statistical concepts in evaluating the gathered data, find the inevitable errors, and qualify the different parameters of the said data set. Ten one-peso coins were weighed carefully on the analytical balance, separated in to two data sets (see Appendix A, Table 2). It is important to use forceps to prevent undesired fingerprints, which can add undesired weight, while handling the coins. The Ohaus Analytical Plus Series analytical balances were used for the weight analysis. An analytical balance is a weighing tool with a capacity that ranges from 1 g to a few kg with a precision of at least 1 part in 105 at maximum capacity.(2) The statistical parameters of both sets can be found on Table 1.

Table 1 Calculated Values of Several Statistic Parameters Parameter| Data Set 1| Data Set 2| Mean (X)| 5.3797 0.0005| 5.3866 0.0005| Standard Deviation (S)| 0.01326| 0.00451| Relative Standard Deviation (RSD)| 2.4658| 8.3728| Range (R)| 0.0376 0.0003| 0.166 0.0003| Relative Range (RR)| 6.9892 4.1935| 30.817 18.490| Confidence Limits (CL)| 5.3797 0.01392| 5.3866 0.04222|

The measures of central tendency, accuracy, and precision were evaluated. The measure of central tendency (or central location) is any measure in which the center of the data, arranged in magnitude, is being examined. (4) The mean, one of the most commonly used measure of central tendency, given by the formula below:

(1)

The computed mean for the both sets were also compared, and found that it was relatively lower. This can be rationalized by the fact that the coins sampled were subjected to varied conditions prior to sampling. Not all coins weighed were newly minted, as some of them were damaged, and have chipped surfaces.

Accuracy is the closeness of the values measured experimentally to the real or true value. It also measures the conformity between a result and its true value. (2) With this in mind, errors (relative or absolute) are calculated as the measure of accuracy.

Precision, on the other hand, characterizes the reproducibility of the measured values, or the relation of the values with each other. (1) The parameter S, or standard deviation, is used to measure precision. It is calculated using the formula:

(2)

It can also be expressed in terms of RSD, or relative standard deviation, in which S is in terms of percentage of the mean.(2) It is in ppt (parts per thousand), and calculated using:

(3)

One measurement that accounts for the indeterminate errors of individual sets is called pooled standard deviation. It is represented by spooled and given by:

(4)

Another measure of precision is the range and RR, or relative range. Simply the difference between the highest and the lowest value obtained, range is used for replicate results. (2) The relative range, as the name states, is in relative terms given by the formula:

(5)

The confidence limit is also used to evaluate data sets. It is a numerical interval around X, or mean, that contains a value with a certain probability. It is given by:

(6)

These parameters are important, but a...

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