Table of Contents
What Is the Third Quartile?
The third quartile (Q3), also called the 75th percentile or upper quartile, is the value below which 75% of the data falls. Together with Q1 (25th percentile), Q2 (median), and the minimum and maximum, it forms the five-number summary that provides a complete overview of data distribution.
Q3 is important for identifying the upper range of typical values, constructing box plots, calculating the interquartile range (IQR = Q3 - Q1), and detecting outliers. Any value greater than Q3 + 1.5*IQR is considered a potential outlier using the standard box plot rule.
Calculation Method
When the position is not a whole number, linear interpolation between the two nearest values is used.
Five-Number Summary
| Statistic | Percentile | Description |
|---|---|---|
| Minimum | 0th | Smallest value |
| Q1 | 25th | Lower quartile |
| Q2 (Median) | 50th | Middle value |
| Q3 | 75th | Upper quartile |
| Maximum | 100th | Largest value |
Frequently Asked Questions
How is Q3 used in box plots?
In a box plot, Q3 forms the upper edge of the box. The box spans from Q1 to Q3 (the IQR), with the median as a line inside. The upper whisker extends to the largest value within Q3 + 1.5*IQR. Points beyond the whiskers are plotted as individual outliers.
Are there different methods for calculating quartiles?
Yes, there are multiple methods (inclusive, exclusive, interpolation). Different software may give slightly different Q3 values for the same dataset, especially for small samples. The differences are negligible for large datasets. This calculator uses the interpolation method.