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.