Percentiles are the value of the variate which divides the total frequency into “K” equal parts. K is equal to

99
100
101
None of the above

The correct answer is (b) 100.

A percentile is a value that divides a ranked data set into 100 equal parts. The first percentile (percentile 1) is the value that separates the lowest 1% of the data from the highest 99%. The second percentile (percentile 2) is the value that separates the lowest 2% of the data from the highest 98%, and so on. The 50th percentile is the median, which separates the data into two equal halves.

In a set of data with $n$ values, there are $n+1$ percentiles. For example, in a set of 10 values, there are 11 percentiles: percentile 1, percentile 2, …, percentile 10, and percentile 11.

The value of the variate which divides the total frequency into “K” equal parts is called the $K$th percentile. Therefore, the value of the variate which divides the total frequency into 100 equal parts is called the 100th percentile, or the median.