Measures of Central Tendency, Essay Example

In most statistical problems, Group B would be deemed the more desirable group, with less overall variance, a higher median value which nearly matches its arithmetic mean, and much greater predictability. Group A has both the highest score (100) and the lowest (34), with a lower median score (67).  Group B is far more consistent, with a median of 78 and both the lowest score (64) and highest (92) within fourteen percent of the median. Unfortunately, the greater consistency of Group B does not recommend it over Group A in this exercise, since both groups had average scores of 78.8 percent, and assuming the test scores are accurate indicators of the expected performances of the two groups, they should theoretically perform identically.  The only benefit to consistency in this case is that the mistakes would be more evenly distributed among the Group B workers, in contrast to the perfect score in Group A being offset by the abysmal laborer with 34 percent.  Despite the greater statistical nicety and simplicity offered by choosing group B, there is no actual advantage in this case.  All data indicates that given the same set of tasks, each group would make the same amount of mistakes.  This being the only data on the groups’ projected performance, there can be no clear advantage with either group.  However, with more data, a solution would present itself.  If, for instance, it was made clear exactly how costly the hypothetical accidents actually are, it could be determined that it is more cost efficient to hire Group A and have the five lowest scoring employees sit idle while the others worked.  The upper half of Group A averages at above 97 percent; if it is more productive to field five near-perfect workers and pay the incompetent ones to do nothing, this would be a solution to the problem.  There is not enough data to support whether this would be cost-effective, but as only Group A could be managed this way to experimentally discover the relative worth of working with the top five or six candidates, analysis would suggest that Group A has a slight statistical advantage over Group B, if the aforementioned possibility is an option.  Group B’s greater consistency is a disadvantage in this situation, because the removal of its lowest-scoring employees does not create such a dramatic shift in averages.  The only method of measuring central tendencies that matters in this exercise is arithmetic mean, which is identical, and the only possibility of gaining an advantage is not a purely mathematical exercise at all, merely a suggestion on removing the lowest performers to reduce the number of accidents.  Unlike most forms of statistics, an idle worker in this case does not have a value of zero, but rather 100 percent- that is, he will make no mistakes at all.  Productivity, which is not the same as accuracy, will suffer, but perhaps not efficiency.