Application of Statistical Concepts in the Determination of Weight Variation in Samples
National Institute of Geological Sciences, College of Science
University of the Philippines, Diliman, Quezon City, Philippines
Date Submitted: April 23, 2013
This experiment aimed to determine the exact weight of a 25-centavo coin through weighing out replicate samples on an analytical balance using the method of weighing by difference. The samples were divided into two data sets and analyzed using statistical concepts for comparison. After applying statistical parameters to the data obtained, outlying values were discarded from the data to ensure the ...view middle of the document...
7873 | 0.466 | 0.7466 | rejected |
| L: 3.5371 | 0.466 | 0.1239 | accepted |
The mean is the most common measure of central tendency. It is simply the sum of all observed values divided by the number of values.  Measuring the mean aims to determine what is the center or middle of a distribution. “The value of the mean gives an estimate of the value of dispersion.”  It can be seen in Table 2 that the means of Data Set 1 and Data Set 2 differ only after the 2nd decimal place. This means that the middle of distribution in both data sets are almost the same.
To measure how precise the results of the experiment, standard deviation (s) was measured. The standard deviation is just the positive square root of the variance. It indicates how the results vary from each other. The larger the s value, the more dispersed the data is.  The values of s for both data sets were relatively small which could mean that the samples from the experiment did not greatly differ from each other.
Table 2. Statistical Parameters
| Data Set 1 | Data Set 2 |
mean | 3.5764 | 3.5788 |
s | 0.024002 | 0.019105 |
RSD | 6.7113 | 5.3384 |
R | 0.2502 | 0.2502 |
RR | 69.96 | 69.96 |
CL (95%) | 3.5764 ± 0.025183 | 3.5788 ± 0.013654 |
s pooled | 0.020866 |
Another measurement of precision that was used in this experiment was range (R). It is the difference between the highest and lowest value in the data set. It is useful for illustrating measures of precision because it is independent of the sample size. However, it is a poor method for estimating population dispersion because it is badly affected by errors which cause outliers.  The calculated range for this experiment was the same for both Data Set 1 and 2 which further indicate that the highest and lowest values were the same and justifies that the samples were not dispersed.
Confidence limits or confidence interval is the range in which the true value of a measurement lies. “The interval estimate gives an indication of how much uncertainty there is in the estimate of the true mean. The narrower the interval, the more precise is the estimate.” The true mean of Data Set 1 lies between 3.5512 and 3.6016 while in Data Set 2, it lies between 3.5651 and 3.5925. The confidence interval in both data sets were narrow which implies that the estimate was accurate. Furthermore, the 95% level of confidence used in this experiment means that there is a 95% probability that the interval contains the true mean.  It is only valid when determinate errors are absent in the experiment. 
On the subject of errors, an error is defined to be the difference between the test result and the true value. There are three major types of which according to their character and magnitude. Gross or erratic errors are suspected when one value varies greatly from the others. It widely disagrees with the true value and is due to the carelessness of the person handling the experiment. An example of which is...