** Percentile vs Percentage **

Percentile and percentage are important when describing quantities. Percentage is just an arithmetic concept that allows comparison between different fractions and easier understanding. Percentile is a statistical concept that denotes a subset consisting a percentage from the population/ distribution.

**Percentage**

Percentage in mathematics is a concept used to summarize and clearly express data related to fractions and ratios. In general, percentage of a certain quantity is a fraction of a 100. For example consider the percentage 5%. This is equivalent to the fraction 5/100. Since the number hundred is a power of ten, the mathematics involved is convenient, and a fraction involving hundred is easier to understand.

The general formula for calculating the percentage can be given as:

x/y × 100 = ___ %

A fraction or a ratio multiplied by hundred gives the percentage. The percentage value in general is a value between 0 and 100. However, this can be extended into values beyond 100. The percentage is always signified by placing the percent symbol % at the right hand side of the number. The x and y can be any real number, with the exception of y excluding the value 0. The actual value of the fraction (x/y) depends on the problem concerned.

Any fraction or a ratio can be transformed into a percentage. This provides a rather convenient way of comparing the fractions or ratios since each percentage represent a fraction of a hundred (the denominator is always 100).

**Percentile**

Percentile is a value at or below which a certain percentage of the distribution lies. There are several commonly used interpretations of the percentiles. If an element is in the nth percentile, it implies that n% of the distribution lies below that element.

For example, if a student is in the 80th percentile of a mathematics test, it implies that 80% of the students have got marks below that student.

The 25th percentile is also called the first quartile, and the 50th and 75th percentiles are second and third quartiles respectively.

**What is the difference between Percentile and Percentage?**

• Percentage gives a quantity as a fraction of a hundred while percentile gives you the percentage that lies below the score or values of a given distribution.

• Percentile is a concept based on the percentage.

• Percentage can be calculated in any fraction while percentile has meaning only when applied to a population (such as scores of cricket players below 30 years)

• Percentiles separate the population into 100 subsets.