Three terms that students often confuse in statistics are percentiles, quartiles, and quantiles.
Here’s a simple definition of each:
Percentiles: Range from 0 to 100.
Quartiles: Range from 0 to 4.
Quantiles: Range from any value to any other value.
Note that percentiles and quartiles are simply types of quantiles.
Some types of quantiles even have specific names, including:
- 4-quantiles are called quartiles.
- 5-quantiles are called quintiles.
- 8-quantiles are called octiles.
- 10-quantiles are called deciles.
- 100-quantiles are called percentiles.
Note that percentiles and quartiles share the following relationship:
- 0 percentile = 0 quartile (also called the minimum)
- 25th percentile = 1st quartile
- 50th percentile = 2nd quartile (also called the median)
- 75th percentile = 3rd quartile
- 100th percentile = 4th quartile (also called the maximum)
Example: Find Percentiles & Quartiles
Suppose we have the following dataset with 20 values:
Using statistical software (like Excel, R, Python, etc.) we can find the following percentiles and quartiles for this dataset:
Here’s how to interpret these values:
- The 0 percentile and 0 quartile is 3.
- The 25th percentile and 1st quartile is 8.5.
- The 50th percentile and 2nd quartile is 16.5.
- The 75th percentile and 3rd quartile is 23.5.
- The 100th percentile and 4th quartile is 37.
When to Use Percentiles vs. Quartiles
Percentiles can be used to answer questions such as:
What score does a student need to earn on a particular test to be in the top 10% of scores?
To answer this, we would find the 90th percentile of all scores, which is the value that separates the bottom 90% of values from the top 10%.
What heights encompass the middle 40% of heights for students at a particular school?
To answer this, we would find the 70th percentile of heights and 30th percentile of heights, which are the two values that determine the upper and lower bounds for the middle 40% of heights.
Quartiles can be used to answer questions such as:
What score does a student need to earn on a test to be in the top quarter of scores?
To answer this, we would find the 3rd quartile of all scores, which is the value that separates the bottom 75% of values from the top 25%.
What is the interquartile range of a given dataset?
The interquartile range (IQR) is the range of the middle 50% of data values. To find the IQR for a given dataset, we can calculate 3rd quartile – 1st quartile.