Q1
College/University
Definition
In statistics, Q1 is known as the first quartile or lower quartile. Quartiles divide up a data set into four equal sections. Q1 is the middle value in the first half of the data set. It is also known as the first 25% of a data set. Remember that the data has to be sorted first before quartiles can be found.
Worked examples
\(\)Data: \( 3, 7, 8, 12, 15, 18, 22, 25, 30 \quad \)→\( \quad Q1 = 8\)
Q1 is the median of the lower half (3, 7, 8, 12) — the middle value of the first four numbers.
\(\)Data: \( 2, 5, 9, 11, 14, 16, 20, 23 \quad \)→\( \quad Q1 = \frac{5 + 9}{2} = 7\)
With an even-sized lower half (2, 5, 9, 11), Q1 is the average of the two middle values.
Common mistakes
- Finding Q1 from unsorted data → Sort the data first, then find Q1 Quartiles require sorted data; otherwise you find the wrong position.
- Taking 25% of the largest value instead of finding the position → Q1 is the value at the 25% position in sorted data Q1 marks the first quartile position, not 25% of the maximum.
- Including the median in both halves when splitting the data → Exclude the median when the count is odd, then find Q1 in the lower half Different methods exist; follow your course convention for handling the middle value.
Where you'll use it next
You'll use Q1 with Q3 to calculate the interquartile range (IQR) and identify outliers in box plots, and it appears in descriptive statistics throughout data analysis and probability.
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