# How to find Quartiles, Deciles, and Percentiles Ungrouped Data

In this lesson, I will talk about triangle inequalities, exterior angle, and hinge theorem. These theorems can help us arrange the sides and angles of a triangle from smallest to largest.

##### Quartiles

The quartiles of a data set divide the data into four equal parts, with one-fourth of the data values in each part. The second quartile position is the median of the data set, which divides the data set in half. To find the median position of the data set, divide the total number of data values (n) by 2. If there are an even number of data values, the median is the value that is the average of the value in the position and the + 1 position. (If there are an odd number of data values, the median is the value in the position.)

The first quartile is the median of the first half of the data set and marks the point at which 25% of the data values are lower and 75% are higher. The third quartile is the median of the second half of the data set and marks the point at which 25% of the data values are higher and 75% lower.

##### Deciles and Percentiles

Deciles and percentiles are usually applied to large data sets. Deciles divide a data set into ten equal parts. One example of the use of deciles is in school awards or rankings. Students in the top 10% — or highest decile – may be given an honor cord or some other recognition. If there are 578 students in a graduating class, the top 10%, or 58 students, may be given the award. At the opposite end of the scale, students who score in the bottom 10% or 20% on a standardized test may be given extra assistance to help boost their scores.

Percentiles divide the data set into groupings of 1%. Standardized tests often report percentile scores. These scores help compare students’ performances to that of their peers (often across a state or country). The meaning of a percentile score is often misunderstood. A percentile score in this situation reflects the percentage of students who scored at or above that particular group of students. For example, students who receive a percentile ranking of 87 on a particular test received scores that were equal to or higher than 87% of students who took the test. For those who do not understand these scores, they often mistake them for the score the student received on the test.

###### Useful Resources

Practice what you’ve learned in these problems.

Exercises 1

Exercises 2

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