Statistics is an essential part of our lives. It helps us represent or understand different kinds of data. It involves various formulas, charts, tables, or diagrams that help organize extensive data into an organized form to become understandable.
Percentile is one such integral part of statistics that are widely used. It represents a set of data below it and is equivalent to its value. In simple words, the nth percentile represents that out of all the data included, n percent of the total data is below it. There are many ways percentiles are used in our daily lives, such as biometric measurements, health test reports, academic test reports, government public reports, and much more.
For example, in a statewide academic test, you receive your result as 98th percentile. Your total marks out of 500 are 492. This means that out of all the students who took the test, 98 percent scored marks below or equivalent to 492. Another student who got 20th percentile scored 115 marks out of 500. This means that 20 percent of students scored marks identical to or below 115.
What is a percentile?
Percentile represents a number where a certain percentage of scores falls below that number. For example, if you are the fifth tallest person in a group of 20, that means 75% of people are shorter than you, so you are at the 75th percentile.
The majority of people misinterpret percentile as a percentage. However, both are different and are used in different ways to represent data. While the percentage represents a fraction of a set of data, the percentile represents a value below which an equivalent percentage of the total data is found.
The difference between the two will be clearer with the help of this example. In a class of 50 students, an exam was conducted with a maximum score of 100 marks. A student scored 80 percent. This means that they answered four questions correctly out of every five questions. Many students could have scored the same percentage. However, another student scored in the 80th percentile. This represents that this student scored marks higher than 80 percent of the total students in the class, that is, 40 students.
Therefore, the percentage represents how much a student scored in the exams, and the percentile represents how well they performed or the student’s rank compared to others.
How To Calculate Percentile?
To calculate percentile you need to find the number of values below the score and divide it with a total number of scores.
Percentile = (number of values below score) ÷ (total number of scores) x 100
For example, in a class, the heights of 16 students are recorded. Their heights are then arranged in ascending order. The following is the data that we got:
4.10, 4.10, 4.10, 4.11, 5.0, 5.0, 5.0, 5.1, 5.2, 5.2, 5.2, 5.2, 5.3, 5.3, 5.4, and 5.4
If we want to find which height marks the 50th percentile, we will put in the values from the data in the above formula.
n= (50/100) x 16
To learn more, visit our article How to calculate percentile in Excel
Therefore, the 8th value in the above data, 5.1, marks the 50th percentile. This means half of the students have heights shorter than those whose height is 5 feet 1 inch or 50 percent of the students’ height is equal to or below 5.1 feet.
Quartiles, Deciles and Percentiles
When we arrange the data in ascending order ( putting the lowest value first), we can mark some of the percentile values with the help of the first quartile, the median, and the third quartile. These three points divide a set of given data into four equal parts.
- The first quartile implies that one-fourth of the total data is below this point. For example, one-fourth of 100% is 25%. Therefore, the first quartile indicates the 25th percentile of a set of information.
- The median: The median indicates the middle value or middle point in a given data. This means that half, or 50%, of the data, lies above or below it. Therefore, the median marks the 50th percentile of a set of data.
- The third quartile: The third quartile indicates the end of three-fourths of the given data. This means that 75% of the data lies below this point. Therefore, the third quartile indicates the 75th percentile of a given set of data.
Another way to mark percentiles is by using deciles. When you arrange data by deciles, it implies that every decile marks 10% of the given data. This means the nth decile indicates that nx10%of data lies below it. For example, the 1st decile demonstrates that 10% of the provided data lies below it, and the 2nd decile suggests that 20% of the total data is below it. Therefore, the first decile marks the 10th percentile; the 2nd decile marks the 20th percentile. Through deciles, more percentiles can be characterized as compared to quartiles.
Where Can You Apply Percentile?
Whenever there is a large set of data that needs to be presented in a readable form, percentile can help you solve the issue. A perfect example of how percentile helps represent the data in a clarified form can be seen through the SAT scores. It focuses on how well the students performed and where they stand compared to other students who took the exam.
For example, a student who took the test scored 95 percent. This score is considered impressive and requires a lot of effort to score this much. But how well did the student performance compare to other students? This can be determined with the help of percentile. For example, if this 95 percent score marks the 40th percentile, then it implies that 60 percent of the students scored more than them, or only 40 percent of students scored marks less than or equal to 95 percent.
Another application of percentile can be seen in pediatric clinics where it is used to compare the growth of infants and children to others in the same age group. For example, a pediatrician generally measures the height and weight of the children and represents this information in percentiles. This helps parents understand how steady and appropriate their child’s growth is compared to other children.