Given ordered data, a percentile represents a value that is better than that percentage of others.
e.g. if you scored the 80th percentile, that means your score is better than or equal to 80% of everyone else who took it.
The formula is:
If i is a whole number, then you take that value in the order, else
you take the mean of i and i+1.
To calculate a value for a given percentile, knowing only the mean and standard deviation, the formula is where z is the value from a z-table corresponding to the target percentile.