PENNY PINCHING: STATISTICAL TREATMENT OF DATA

Objective

Interpretation is one of the important steps for a chemical analysis. Upon receiving raw data, anyone whether scientists or non-scientists can give some thoughts about the results, such as the similarity or difference between the values or the connection between measurements. Scientists are believed to give a better interpretation as they are able to recognize a significant difference between raw data and final results. These results, which are mainly based on the mean values, average values, and standard deviations, however, can still be biased and misinterpreted without using appropriate statistical tools, such as the Q test and the Student’s t test. The Q test allows us to determine if a value can be discarded or retained, while the Student’s t test is used to determine the uncertainty and confidence associated with the assignment of a value. These analysis tools are proved to be very helpful as the data and results can be interpreted in a less biased manner. In this experiment each group of students obtained a sample of 20 pennies. Each penny was weighted and the mass was recorded along with the year of penny. The Q test was performed to determine if any values would be rejected. The whole class data set was used to construct a frequency histogram and two distinct distributions in the penny masses were noticed. The Student’s t test was then used to evaluate whether the two distributions of pennies really represent two distinct sets of pennies or simply one set of penny weights. By using these two statistical tests, it was concluded that there is a correlation between the year of the pennies and the apparent bimodal distribution of penny weights. Data

Table 1. Individual Data for the masses and the years of pennies (n=16 measurements). |Pennies |Year |Weight (g) | |1 |1987 |2.4533 | |2 |2004 |2.4691 | |3 |1988 |2.4723 | |4 |1993 |2.4760 | |5 |1999 |2.4763 | |6 |2002 |2.4832 | |7 |1997 |2.4912 | |8 |1998 |2.5033 | |9 |1993 |2.5055 | |10 |2002 |2.5155 | |11 |1985 |2.5161 | |12 |1984 |2.5568 | |13 |1975 |3.0969 | |14 |1979 |3.1063 | |15 |1973 |3.1316 | |16 |1982 |3.1873 |

Table 2. Frequency Table for Class Data of the penny masses over the mass range of 2.300g and 3.300g (n=176 measurements). |Range (g) |# of pennies | |Range (g) |# of pennies | |2.300 to 2.325 |0 | |2.800 to 2.825 |0 | |2.325 to 2.350 |0 | |2.825 to 2.850 |0 | |2.350 to 2.375 |1 | |2.850 to 2.875 |0 | |2.375 to 2.400 |0 |...