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

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Statistics is a mathematical science dealing with the collection, organization, analysis, interpretation, and presentation of data. It provides a more accurate way of expressing data rather than mere observation. This experiment used the different statistical concepts such as the Q test, mean, standard deviation, relative standard deviation, range, relative range, and confidence limits or confidence intervals.

The results generated from these tests are used as a basis to check whether the values obtained from weighing 10, 25 centavo coins using an analytical balance and which were grouped into two data sets, are acceptable or not. It can be seen that when the statistical concepts were applied to data set 1 and data set 2, the resulting values obtained do not greatly vary. However, it can’t be proven that the results do not differ significantly since there was no test performed to check this.

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Different weights were obtained from the 10- 25 centavo coins using the analytical balance. Each weight is considered as a single sample. The samples were grouped into two data sets. The first dataset contains six samples while the second data set contains 10 samples. The table below shows the two data sets with their corresponding samples.The Q test was performed for each of the data sets. Other statistical parameters were also calculated. When one or more of the measured values obtained within a set is/are different from the rest, the Q test can be used to check if the suspected value or values should be retained or rejected (chem. uoa. gr). However this is only used for a small number of samples or replicates in a given set.

Hence, this test is used in this experiment. Furthermore, the Q test is an example of a significance test. The outcome of this test is the acceptance or the rejection of the null hypothesis. For the purpose of this paper, the null hypothesis would be that, there is no significant difference between the suspected value or values from that of the rest of the values obtained.

As mentioned, other statistical parameters were also calculated. These include the mean, standard deviation, relative standard deviation, range, relative range, and confidence limits (at 95% confidence level) The first of these other parameters being tested is the mean. The mean is one of the three parameters under measures of central tendency. According to the Australian Bureau of Statistics, “a measure of central tendency is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or center of its distribution”.

One possible reason that can account for the difference in weight between the weight values obtained from the experiment from that obtained from the BSP website, is the year that the coins were manufactured and the percent material composition of the 25 centavo coin. It could be that BSP created the coins used in the experiment in a different year and with a different per cent material composition thus it weighed less than that of the current and official weight of the 25 centavo coin.

However, there is no compelling evidence for this since the BSP website does not have any information as to when the coins weighing 3. g were made or if it has a different per cent material composition from the previous coins manufactured. The second and third parameters are the standard deviation and the relative standard deviation. These two statistical parameters are under the measures of precision. Precision refers to how close the results obtained from the samples are to each other (fao. org). By this, the standard deviation can be defined as the precision in a series of repetitive measurements around the mean (files. chem. vt. edu).

For the purpose of this paper, only the resulting values for the standard deviations of datasets 1 and 2, which are 0. 04024g and 0. 0355g, respectively, will be interpreted since the standard deviation values generated are not that large. Since standard deviation refers to how close the values of the sample in a data set are around the mean, a high standard deviation value means that the value of each sample in a data set are widely scattered, while a low standard deviation value means that the value of each sample in a data set are close to the mean (fgse. nova. edu).

When the standard deviation value was applied to each value of a sample in the two data sets of the experiment, the resulting values obtained were close to the mean. Hence, there are no deviant values of the individual values of the samples of each data set. The fourth and fifth parameters are the range and relative range. Like the standard deviation and relative standard deviation, these two are under the measures of precision. The range is just the difference between the highest and lowest sample values in a data set and is the simplest measure of spread (Statistics. aerd. com). The range is easy and useful, however its use is limited. On the other hand, relative range, just like relative standard deviation, is expressed in relative terms.

By this, the confidence interval is defined as the estimated range of values which is likely to include an unknown population parameter (Easton and McColl). Furthermore, Easton and McColl said that, “the width of the confidence interval gives some idea about the uncertainty of the unknown parameter. A very wide interval may indicate that more data should be collected before anything very definite can be said about the parameter”.

When the results of the parameters tested for dataset 1 and data set 2 are compared with each other, it can be seen that, the results from dataset 1 and 2 do not greatly vary. From the results obtained from the Q-test up to the confidence limits or confidence intervals, the results are close to each other. However, the above statement is just based on observation since there is no test performed to check whether the resulting values from the test parameters obtained from dataset 1 and 2 differ or do not differ significantly with each other.