Introduction
The key distinction between percentage and percentile is that the former refers to a numerical value expressed as a percentage, which is, out of 100. On the other hand, percentile refers to the percentage of values that fall below a given value. Comparing quantities is made possible by using the percentage. Positions or ranks are displayed using a percentile.
What is called a Percentage?
Percentage is a mathematical quantity that is expressed as a fraction of a whole number, 100. The word ‘percent’ is used to denote percentage. The denominator value of 100 is denoted by the symbol ‘%’. Percentage can also be expressed using decimals or fractions. A percentage is typically used in the comparison process to distinguish between the quantities. It provides details regarding ratio and proportions.
For example, a student has achieved a cumulative score of 40% in his science exam, if he receives 40 out of a possible 100 marks in the exam. The student’s performance on the science exam was scored as 40%.
What is a Percentile?
The percentage of values that fall below a set of values is known as a percentile. The ranking system mainly employs percentiles. It is based on segmenting the normal distribution of values. n\(^{\text{th}}\), where n is a number, is used to represent percentiles.
For example, let’s assume that a student has 50th percentile took a 250 – point test. This clarifies the meaning of the word percentile and shows that, if a student receives a score of 250 on the test, they performed better than 50% of the other students in the class.
What is the difference between the Percentage and Percentile?
Percentage and percentile are two distinct ideas because percentile displays a comparison, while percentage displays an individual score out of 100. A percentile is a relative quantity that compares a given value to the rest of the data that is less than the given specific value. A percentage tells us the value in terms of 100.
To make the concepts clearer, go over the distinctions between percentage and percentile.
Percentage | Percentile |
|---|---|
A mathematical measure that indicates the result as a percentage of 100. | Percentile is a number that can be used to calculate the percentages below it. |
Percent is used to represent the percentage unit %. | The n\(^{\text {th}}\) position, for instance, 20th, represents the percentile unit. |
There are no quartiles in it. | There are quartiles in it. |
Ratios are one way to write a percentage. | Ratios cannot be used to express a percentile. |
Decimals can also be used to represent percentages in writing. | On the other hand, decimal representations of percentiles are not permitted. |
The rank of the numbers is not used to calculate percentages. | The rank of numbers is the foundation of a percentile. |
It is based on a single instance. | It is based on a comparison between a single case and a number of cases. |
It is independent of normal distribution. | The normal distribution is a foundation for percentile. |
How to Calculate the Percentage?
We divide the given value by the total value and multiply the result by 100 to find the percentage of the given value. Since it is easier to understand the data in terms of 100, percentage is frequently used to determine the value in terms of that number.
The formula to find the percentage is: \(\frac{\text{Given value}}{\text{Total value}}\ \times\ 100\)
How to Calculate Percentile?
A relative value called a percentile makes it possible to compare a given value to the rest. This is frequently used in tests that are competitive, where each student performs differently and where each student can precisely know where they stand in relation to the other students. Additionally, companies use percentiles to gauge employee performance in relation to one another and reward the top performers.
The formula to find the percentile is: \(\frac{\text{Number of values below ‘n’}}{\text{Total number of values}}\ \times\ 100\)
Solved Examples
Example 1.
Determine the percentage of each given value.
- 37% of 114
- 48% of 104
- 65% of 212
Solution:
- 37% of 114 = \(\frac{37}{100}\ \times\ 114\)
= \(0.37\ \times\ 114\)
= 42.18
- 48% of 104 = \(\frac{48}{100}\ \times\ 104\)
= \(0.48\ \times\ 104\)
= 49.92
- 65% of 212 = \(\frac{65}{100}\ \times\ 212\)
= \(0.65\times\ 212\)= 137.8
Example 2:
Calculate the percentage of mangoes in a basket of 300 fruits if there are 65 mangoes and the remainder are oranges.
Solution:
To calculate the percentage of mangoes in the basket, we will use the basic formula to find the percentage: \(\frac{\text{Given value}}{\text{Total value}}\ \times\ 100\)
We know that there are 65 mangoes
Number of fruits = 300
So, after substituting the values in the formula,
\(\frac{\text{Given value (Number of mangoes)}}{\text{Total value (Total number of fruits)}}\ \times\ 100 = \frac{65}{300}\ \times\ 100\) = 21.67%
Therefore, the percentage of mangoes in the basket is 21.67%.
Example 3.
Jake is ranked sixth out of 26 students in his class. What is Jake’s class percentile?
Solution:
We use the equation [(Number of students who scored less marks than Jake) ÷ (Total number of students)] x 100 to calculate Jake’s percentile in the class.
Given that there are 26 students overall and that Jake is ranked sixth in the class. So, there are 20 students who scored lower than Jake. (26 – 6 = 20).
As a result, [(Number of students who scored less marks than Jake) ÷ (Total number of students)] x 100 is obtained after substituting the values in this formula.
= \([\frac{20}{26}]\) × 100
= 76.92.
Therefore, Jake’s percentile is approximately equal to 77th.
No, percentiles and percentages are not the same.
The concepts of percentage and percentile are distinct. Percentile can distinguish between the relative score in relation to others and the individual score, while percentage measures with respect to 100. It is therefore impossible to compare these two. For individual scores, percentage is helpful, and percentile is helpful if we want to know how a candidate compares to others. In order to compare relative performance, companies or competitive exams frequently use the percentile method.
A candidate’s exam performance is indicated by their percentage score. This displays his personal grade. A percentile rank reveals the candidate’s relative performance in comparison to the other test-takers.
The percentile is denoted by ‘th’(example: 30th) and the percentage is denoted by ‘%’ (example: 90%).