Question on how to Solve the Probability

Topic : Probability

Question : How to calculate percentile rank for individualseries and group frequency distribution?

Answer :
Computing the Pth Percentile
1. Sort the data.
2. The Pth percentile is found in position P(n + 1)/100.
3. If this position is between observations round to the nearest position (or, if you know how, interpolate between the two).

Example
Let's find the 15th percentile of the starting salary data. Here's the sorted version.
08820 10800 12000 12500 13000 14000 15000 16000 16500 16600 16700 16900 16900 17000 17000 17600 17880 18000 18000 18000 18000 18000 18000 18000 18000 18000 18000 18500 18680 19100 20000 20000 20000 20000 20000 20300 20900 22000 23000 23000 23000 23000 23400 24000 25000 25000 26000 26000 27000 30000 30000 32500 37000 48000
Our position is 15(54 + 1)/100 = 15(55)/100 = 8.25. Round to position 8; the corresponding observation is shown in bold. The 15th percentile is approximately 16000.
A better approach uses interpolation. The 8.25 position is really between the 8 and 9 positions, One-quarter of the way from 16000 to 16500 is
0.75(16000)+0.25(16500) = 16125.
So 16125 is a (better) approximation to the 15th percentile. However, it's not that different from 16000, and either would suffice.

Hope the Explanation will be helpful for you.