Percentile

In this article we shall talk about percentiles or centiles that divide a given set of observations into 100 equal parts. The points of subdivisions being P1,P2, ….. P99. P1 is the value for which one hundredth of the observations are less than or equal to P1 and the remaining ninety nine hundredths observations are greater than or equal to P1 once the observations are arranged in an ascending order of magnitude.

Percentile Formula:

For unclassified data, the pth percentile is given by the (n+1)pth value, where n denotes the total number of observations. So p = 1/100,2/100,… 99/100 for first percentile, second percentile, third percentile Ninety ninth percentile, respectively. In general let’s call thatP_i. For calculating percentile of ungrouped data the following formula can be used:
n  = P_i. N/100 + 0.5, where n = the observation of the ith percentile, P_i = ith percentile (in percent) and N = total number of observations. Here n is also called the rank of the observation. So the answer for the ith percentile would be the nth numbered observation. Another formula used for calculating this rank is
n = (N+1)* P_i/100

Percentile chart:

Percentile charts have various applications in the field of national census, health care, competitive exams etc. These charts are made using a very large number of data and a merit list is prepared based on the percentile chart. For example, a pediatrician would use a height and weight percentile chart to check on the growth of a particular baby based on the national averages. Percentile charts also have their applicability in deciding the ranks in case of competitive exams. For example, GRE score is given not as absolute score out of 200 but as a percentile. That means the person with highest score is treated as 100 percentile and other scores are calculated based on that, so a candidate with 90 percentile would be 10th rank and so on.

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