Quartiles
What are quartiles?
The quartiles of a distribution are a set of five numbers that break data from a continuous variable into four equal parts. They are the 0%, 25%, 50%, 75%, and 100% percentiles of the data, also stated as the minimum value, 25th percentile, median, 75th percentile, and maximum value. The minimum is also called the 0th quartile; the 25th percentile is also called the first quartile, the median is also called the 50th percentile or second quartile, the 75th percentile is also called the third quartile, and the maximum is also called the fourth quartile.
When should you use quartiles?
Sample quartiles are shown on a box plot. The minimum and maximum values are usually the points at the ends of the whiskers, the first and third quartiles are the points at the ends of the box, and the median is the line in the middle of the box.
If you use an outlier box plot, the ends of the whiskers might not extend to the minimum and/or maximum values. If there are potential outliers detected using the IQR rule, the ends of the whiskers extend to the first or last point within 1.5 ´ IQR from the first and/or third quartiles.
You can calculate quartiles whenever you want to break up your data into fourths.
How do you calculate quartiles?
Use the formula for quantiles to calculate percentiles.
Statistical software, like JMP, can also calculate quartiles. Different software might use different formulas. Be sure to check the software’s documentation to find which formula is used.
Examples of quartiles
For the cereal calories data, you can see some common quantiles, including the quartiles, in the figure below.
As another example, examine the quartiles for the data in the in the Univariate Statistics Data. You can visualize the quantiles using the quantile box plot and see the value of some quantiles, including the quartiles, in the Quantiles report.
