What is Percentile?

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 understandable form.

Percentile is a widely used integral part of statistics. It represents a set of data below it and is equivalent to its value. Simply put, the nth percentile represents that out of all the data included, n percent of the total data is below it. Percentiles are used daily in many ways, 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 the 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, 75% of people are shorter than you, so you are at the 75th percentile.

Most people misinterpret the percentile as a percentage. However, both are different and are used to represent data in various ways. While the percentage represents a fraction of a data set, the percentile represents a value below which an equivalent rate of the total data is found.

The difference between the two will be more apparent with the help of this example. An exam was conducted in a class of 50 students 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 means that this student scored higher than 80 percent of the total students in the class, that is, 40.

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 the percentile, you need to find the number of values below the score and divide it by the 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 the values from the data in the above formula.

n= (50/100) x 16

n= 8

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

Quartiles

When we arrange the data in ascending order ( putting the lowest value first), we can mark some percentile values with the help of the first, median, and third quartiles. These three points divide a set of given data into four equal parts.

• The first quartile implies that one-fourth of the 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 set of 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 data set.

Deciles

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% is below it. Therefore, the first decile marks the 10th percentile; the 2nd decile marks the 20th. Through deciles, more percentiles can be characterized than quartiles.

Where Can You Apply Percentile?

Whenever a large set of data needs to be presented in a readable form, percentile can help you solve the issue. A perfect example of how the 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 those 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’s 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 scored marks less than or equal to 95 percent.

Another application of percentile can be seen in pediatric clinics, where it compares the growth of infants and children to that of 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.

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