The results of the Common Admission Test (CAT), used for admissions to the Indian Institutes of Management (IIMs) and other business schools, were announced on Monday. Some 195,000 students took the test, according to a statement by the Indian Institute of Management-Bangalore, out of which 20 candidates were awarded “100 percentile”. Given that IIMs award percentiles up to two decimal places, 20 out of 195,000 students getting “100 percentile” is a mathematical oddity.
“Percentile” is defined as the percentage of data points that have a value strictly less than the given data point. So a data point is in the “50th percentile” if 50% of all data points in the dataset lie below it. A data point in the 99th percentile has 99% of all data points below it. From this point of view, the concept of “100 percentile” is unusual, since it is impossible that 100% of all data points lie strictly below a particular data point.