What is the difference between percentile and percentage :- Percentile and percentage are two different measures of relative position or distribution within a data set. In this response, we will explain how to calculate percentile, how it differs from percentage, and provide examples to help illustrate these concepts.
What is the difference between percentile and percentage?
What is percentile?
Percentile is a measure that indicates the value below which a given percentage of observations in a group of observations fall. It is used to describe the position of a particular value within a distribution. For example, the 75th percentile is the value below which 75% of the observations fall.
To calculate the percentile of a particular value in a data set, you first need to order the data from lowest to highest. Once you have the ordered data, you can find the percentile of a particular value by using the following formula:
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Percentile rank of a value = (number of values below the given value / total number of values) x 100
For example, let’s say you have a data set of 10 values:
5, 7, 8, 9, 12, 14, 16, 18, 20, 21
If you want to find the percentile of the value 14, you would first order the data:
5, 7, 8, 9, 12, 14, 16, 18, 20, 21
The value 14 is the 6th value in the ordered list, so the percentile rank of 14 is:
(5 / 10) x 100 = 50
This means that the value 14 is at the 50th percentile of the data set.
Another way to calculate percentile is by using the following formula:
Percentile = (p / 100) x (n + 1)
where p is the percentile you want to calculate (e.g., 50 for the 50th percentile), and n is the total number of values in the data set. In this example, p = 50 and n = 10, so the percentile of the value 14 would be:
(50 / 100) x (10 + 1) = 5.5
The 5.5th value in the ordered list is between 14 and 16, so we can interpolate to estimate the percentile of 14:
Percentile of 14 = 50 + (0.5 x (60 – 50)) = 55
So, the value 14 is at the 55th percentile of the data set.
What is percentage?
Percentage is a measure of proportion or relative size, usually expressed as a fraction of 100. It is often used to describe the portion of a whole that is represented by a particular value. For example, if 20 out of 100 people in a room are wearing hats, the percentage of people wearing hats is 20%.
To calculate percentage, you need to divide the value you are interested in by the total number of values in the data set and then multiply by 100. For example, if you have a data set of 100 values and 20 of them are greater than 10, the percentage of values greater than 10 is:
(20 / 100) x 100 = 20%
How percentile differs from percentage?
Percentile and percentage are two terms that are often used interchangeably, but they have different meanings and uses. In this article, we will discuss the differences between percentile and percentage.
Percentage is a term that is commonly used to express a part of a whole. It is defined as a number or ratio expressed as a fraction of 100. For example, if a student scored 80 marks out of 100 in an exam, it means that the student has scored 80% in the exam. Percentage is used to represent how much of a quantity is present in relation to the total quantity.
Percentile, on the other hand, is a statistical measure that represents the value below which a given percentage of observations fall. It is used to divide a set of observations into equal parts based on their rank or position. For example, if a student is in the 80th percentile, it means that 80% of the students scored below that student.
To better understand the difference between percentile and percentage, let us consider the following example. Suppose a company has 100 employees, and their salaries range from $20,000 to $100,000. If we want to know how much the top 10% of employees earn, we would use percentile. In this case, the 90th percentile would represent the salary below which 90% of the employees fall. So, if the 90th percentile is $80,000, it means that the top 10% of the employees earn more than $80,000.
If we want to know how much of the company’s total salary is paid to the top 10% of employees, we would use percentage. In this case, we would calculate the total salary paid to the top 10% of employees and divide it by the total salary paid to all employees. This would give us the percentage of the company’s total salary paid to the top 10% of employees.
In conclusion, percentage and percentile are two different statistical measures used to represent different types of data. Percentage is used to represent how much of a quantity is present in relation to the total quantity, while percentile is used to divide a set of observations into equal parts based on their rank or position.