Q3
College/University
Definition
In statistics, Q3 is known as the third quartile or higher quartile. Quartiles divide up a data set into four equal sections. Q3 is also known as the 75th percentile of a data set. Remember that the data has to be sorted first before quartiles can be found.
Worked examples
\(\)Data: \( 2, 5, 7, 9, 12, 15, 18, 20, 23 \quad \)→\( \quad Q3 = 20\)
With 9 sorted values, Q3 is at position 75% through the data—the value separating the top quarter from the rest.
\(\)Data: \( 3, 6, 8, 10, 14, 16 \quad \)→\( \quad Q3 = \frac{14 + 16}{2} = 15\)
When the 75th percentile falls between two values, Q3 is their average.
Common mistakes
- Finding Q3 without sorting the data first → Always sort the data in ascending order before finding Q3 Quartiles are position-based; unsorted data gives the wrong value.
- \(Q3 = \frac{\)max\( + \)min\(}{2}\) → \(Q3\) is the value at the 75th percentile, not the midpoint of extremes Q3 divides the upper 25% from the lower 75%, not the whole range.
- Confusing Q3 with the median (Q2) → Q3 is the 75th percentile; median is the 50th percentile (Q2) Q3 is always greater than or equal to the median in any data set.
Where you'll use it next
Q3 is a building block for box plots, five-number summaries, and the interquartile range (IQR). You'll use it throughout AP Statistics, data analysis, and any course involving descriptive statistics and outlier detection.
Found in 1 StudyPug lesson
Understanding Measures of Relative Standing in Statistics
12th Grade12thStatistics
Explore z-scores, quartiles, and percentiles to gain powerful insights into data distribution. Learn how to interpret and apply these essential statistical tools for effective analysis.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026