Percentiles are ways of using proportions and relative ranking or comparing values of a set of data or observations. Example, the 50th percentile means that 50% of the observations falls below that point.
1. Know the meaning of use for , and recognize examples of percentage, percentile, and percentile rank.
A percentage is parameter with unit as, % that represents the proportion of a value compared to another number relative to the other number being consided a whole.
Percent of a number, x out of another number n is:
, Example 123 is what percent of 246?
123 is 
Percentile is the value below which a stated percentage of the observations lie.
Example if 64 of 80 students scores less than 70 points on a
test, then 
Then 70 points is the 80% percentile, i.e. 80% of the students had grades below 70 point.
The 80% percentile is written as P80 .
To find the mth percentile of a group series of numbers
See Excel program to calculate percentiles for set of data values.
The percent rank is a percent number that indicates the percentage of observations that falls below a given value.
It is best used when describing individual cases. Example, if you score a 612 on the Verbal Portion of the GMAT and your percentile rank is 66, then 66% of the people that took the verbal portion of the GMAT scored below 612.
The percentile rank m of Pm .of a data value, x is approximated from the formula:
2. Know the reference points needed to interpret percentage, percentile, and percentile rank.
For percentage it is useful to know the total possible values, observations etc. If you score 100% on an exam its would be useful to know if there were 2 questions or 100.
To interpret a percentile rank, it is helpful to know the number possible.
When interpreting the percentile rank it is useful to know the charateristics of the reference group to which the scores are been compared. If you being a high school student score 100% on a test for graduate students, the reference group could be bias toward you performing better on the test.
3. Know the measured scales used for percentage, percentile, and percentile rank and the types of statistical analysie appropriate for each.
Percentage is measured on a ratio scale (proportions). The original values of the varible is not reflected in the percentage statistics parameter.
0% means no observation and 100% means all observation.
There are no limitations in ussing percentages in statistical analysis.
Percentiles are measured on the same scale as the original variable. They are not often used to calculate other statistics. Example the 80% rank (P80 .) is 165.
Percent ranks are reported on ordinal scale and not appropriate for statistical analysis. Example it would be inapropriate to compare the average of a set of percentile ranks or their correlation with other percentile ranks. Possible values for percentile ranks are 1 to 99 integers (whole numbers between 1 and 99). Percentile ranks of ) and 100 are not used.
4. Know the meaning of quartile.
A fractile is that point below which a stated fraction (or decimal equilvalence) of the values lie.
So 165 is the 80th percentile (80/100) or .80-fractile.
The median as the 50th percentile is the same as the 0.50-fractile.
The are 3 special percentiles called the quartiles, which divide the data into four groups of equal size.
The first quartile is the same as the 25th percentile or 0.25-fractile.
The second quartile is the 50th percentile or the 0.05-fractile.
The third quartile equals the 75th percentile or 0.75-fractile
(there is no fourth quartile).