# Definition of a Percentile in Statistics and How to Calculate It

Percentiles are a tool used in statistics to comprehend and analyze data. A data set’s nth percentile is the number below which n percent of the data falls. Percentiles are often used daily to comprehend numbers such as test results, health indicators, and other metrics. An 18-year-old man who is six and a half feet tall, for instance, is in the 99th percentile for height. This indicates that 99 percent of the guys aged 18 are at least six and a half feet. On the other hand, a boy aged 18 who is just five and a half feet tall is in the 16th percentile for his height, which means that only 16% of men of the same age are the same height or less.

Key Facts: Percentiles

• Data may be understood and interpreted using percentiles. They show the range of values below which a certain proportion of the data in a collection is found.
• The formula n = (P/100) x N, where P is the percentile, N is the number of values in a data collection (ordered from least to most significant), and n is the ordinal rank of a particular value and may be used to determine percentiles.
• To comprehend exam results and biometric measures, percentiles are routinely utilized.

What Percentile Means

It is essential to distinguish percentiles from percentages. In contrast to percentiles, percentages are the values below which a certain proportion of the data in a data collection is discovered; they are used to describe fractions of a total. Practically speaking, there is a big difference between the two. For instance, a student may score 75% on a challenging test. This indicates that he answered three out of four questions correctly. A kid with a score in the 75th percentile, however, got a different score. This percentile indicates that the student outperformed 75% of the other test-takers in grade. In other words, the percentile score shows how well the student performed from other students, whereas the percentage score shows how well the student performed on the test.

Percentile Formula

The following formula may be used to generate percentiles for the values in a given data set:

n = (P/100) x N

Where n is the ordinal rank of a specific value, P is the percentile, and N is the number of items in the data collection (with the values in the data set sorted from smallest to most significant). Consider a class of 20 students who just took a test and had the following scores: 75, 77, 78, 78, 80, 81, 82, 83, 84, 84, 84, 85, 87, 87, 88, 88, 88, 89, 90. A data set containing 20 values may represent these scores: 75, 77, 78, 78, 80, 81, 82, 83, 84, 84, 84, 85, 87, 87, 88, 88, 88, 89, 90.

By substituting known numbers into the formula and figuring out n, we can get the score that corresponds to the 20th percentile:

n = (20/100) x 20

n = 4

The score of 78 is the fourth number in the collection of data. This indicates that a score of 78 represents the 20th percentile, which implies that 20% of the class’s pupils had a grade of 78 or below.

Deciles and Common Percentiles

The median, first quartile, and third quartile of a data set arranged in increasing magnitude may be divided into four parts. One-fourth of the data is below the first quartile, which is where it is located. Half of the data are below the median, precisely where the center of the data set is placed. Three-fourths of the data are below the third quartile.

Percentiles may be used to express the median, first quartile, and third quartile. The median represents the 50th percentile since half of the data is less than the median, and one-half is equal to 50%. Since 25% is equivalent to one-fourth, the first quartile represents the 25% percentile. The 75th percentile is in the third quartile.

Along with quartiles, deciles are typical methods of grouping data collection. Each decile represents 10% of the data set. As a result, the first decile represents the 10th percentile; the second decile represents the 20th percentile, etc. Deciles provide a means to divide a data set more evenly than quartiles while avoiding the need to divide it into 100 equal parts as with percentiles.

Applications of Percentiles

Numerous applications exist for percentile scores. Percentiles are valid whenever data collection has to be divided into manageable pieces. Furthermore, they are often used to analyze test results, such as SAT scores, allowing test takers to contrast their performance with that of other students. A student could get 90 percent on a test, for instance. That looks pretty great, but it becomes less so, considering that only 20% of the class scored 90% or below. A score of 90% corresponds to the 20th percentile.

Children’s growth charts are another place where percentiles are used. Pediatricians often provide a percentile score in addition to a physical assessment of a patient’s height or weight. A percentile is utilized when comparing a child’s weight or height to other kids of his or her age. This enables a valuable comparison so parents may determine if their child’s development is typical or atypical.