Percentile data point can be applied to evaluating the scores of students who took the different tests. If most students who took form B are on the lowest percentile while students who took Forms A and C then it implies that the test was the hardest. However, if there is no unique pattern of the distribution of students who took the different forms, then there is no evidence that Form B was the hardest. The student’s argument will be wrong.
Mean, median and mode are measures of central tendency (Bauer, 2009). The mean is the average of a given dataset. It is computed by summing up all the individual values and dividing it by the number of elements in the dataset (Bauer, 2009). The median is the number that is in the middle when the values are arranged in an ascending or descending manner. If the count of elements is odd, it is computed finding the number that results in equal elements on either side of the number when arranged in an ascending or descending manner. However, if the count of numbers is even, it is the average of the two middle elements. The mode is the element that recurs the most is a given dataset. The mode is only possible if there is a number that occurs more than once in the dataset (Bauer, 2009).
The most beneficial in case there are extreme outliers is median and mode. Mean is not reliable because it is a function of all numbers in the dataset including the extreme outlier (Bauer, 2009). Therefore, it will not be a true representation of the data. The mode can be more than one in case there is a tie of the element that recurs the most.
References
Bauer, J. (2009). Statistical Analysis for Decision Makers in Healthcare. New York: CRC Press.
