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# Percentile

In statistics, percentile calculations get computed for data sets when there is a need to organize data into different rankings. However, defining this term is not a simple task. Commonly there are two ways to define a percentile. The first states that a percentile represents the smallest value in a range and anything else which is less than that value1. The second definition is similar to the first except that the value in that percentage range classifies any value which is less than or equal to it1. A third way of dealing with percentiles, combines both of these definitions and is the method which will be exemplified here.

The primary objective of the percentile concept is to detail how an individual measurement or score fits in relation to a larger population2. When using percentiles, any value must fall somewhere between 0 and 100.

For example: You are given this data set which represents the final grades of a first year undergraduate calculus class. There are 30 students, so each value can be ranked from 1 through to 30. With the lowest value 48 representing rank 1 and the highest value 95 equaling rank 30.

Grades: 60, 90, 95, 92, 80, 85, 75, 48, 75, 78, 84, 72, 72, 66, 58, 78, 78, 88, 76, 74, 60, 56, 90, 86, 70, 88, 68, 76, 80, 70.

What is the 50th percentile? In this case, that would be equal to the median. The median of this data set is equal to 76% and therefore, 76 will represent the 50th percentile for the class.

What percentile range does the score 88 fall into? Well when analyzing the data set, it can be seen that the score 88 has 24 scores below it. To find the percentile, divide 24 by the total number of scores which is 30. 24/30 = 80 and thus, the score 88 falls into the 80th percentile range.

Reference:

1. http://knowledge.sagepub.com.proxy.queensu.ca/view/researchdesign/n310.xml?rskey=9h55JF&row=4

2. http://knowledge.sagepub.com.proxy.queensu.ca/view/epidemiology/n345.xml?rskey=9h55JF&row=2

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