Quartile Calculator
Calculate Q1, Q2 (median), and Q3 for a data set. Also displays the interquartile range and five-number summary.
Enter a data set to calculate quartiles.
Quartile Definitions
Q1 = 25th percentile (lower quartile)
Q2 = 50th percentile (median)
Q3 = 75th percentile (upper quartile)
IQR = Q3 − Q1
Q2 = 50th percentile (median)
Q3 = 75th percentile (upper quartile)
IQR = Q3 − Q1
How to Find Quartiles
- Sort the data in ascending order.
- Find Q2 (median): the middle value.
- Find Q1: the median of the lower half (below Q2).
- Find Q3: the median of the upper half (above Q2).
Example: Data: 7, 15, 36, 39, 40, 41
Q2 (median) = (36 + 39) / 2 = 37.5
Q1 = median of {7, 15, 36} = 15
Q3 = median of {39, 40, 41} = 40
IQR = 40 − 15 = 25
Q2 (median) = (36 + 39) / 2 = 37.5
Q1 = median of {7, 15, 36} = 15
Q3 = median of {39, 40, 41} = 40
IQR = 40 − 15 = 25
Five-Number Summary
A five-number summary consists of: Minimum, Q1, Median (Q2), Q3, Maximum. It provides a concise description of the data distribution and is the basis for box plots.
FAQ
What are quartiles used for?
Quartiles divide data into four equal parts and help identify the spread and center of a distribution. They are used in box plots and to detect outliers.
How are outliers identified using quartiles?
A common rule: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are considered outliers.
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Last updated: 2026-08-08