Quartile Calculator
Calculate Q1, Q2 (median), Q3, IQR, and five-number summary. Includes box plot visualization and outlier detection.
Formula:IQR = Q3 - Q1
Results
Median (Q2)
42.5000
50th percentile
Q1 (25th)25.7500
Q3 (75th)58.7500
IQR33.0000
Min12.00
Max120.00
Range108.00
Enter Your Data
18 numbers entered | Range: 12.00 to 120.00
Five-Number Summary
Min
12.00
Q1
25.75
25%
Q2 (Median)
42.50
50%
Q3
58.75
75%
Max
120.00
IQR
33.00
Range
108.00
Mean
45.72
Count
18
Box Plot Visualization
12.0
Q1
Q2
Q3
120.0
Box (Q1 to Q3)
Median (Q2)
Whiskers
Outliers
Outlier Detection (IQR Method)
Lower Fence
-23.75
Q1 - 1.5 x IQR = 25.75 - 49.50
Upper Fence
108.25
Q3 + 1.5 x IQR = 58.75 + 49.50
Outliers Detected (1 total)
Above upper fence: 120
Deciles divide data into 10 equal parts
Sorted Data
1215182225283035404548505560657085120
BlueMedianLightQ1/Q3RedOutliers
Quartile Formulas
Quartile Positions
Q1 position = 0.25 x (n-1) + 1
Q2 position = 0.50 x (n-1) + 1
Q3 position = 0.75 x (n-1) + 1
IQR & Outliers
IQR = Q3 - Q1
Lower Fence = Q1 - 1.5 x IQR
Upper Fence = Q3 + 1.5 x IQR
Results
Median (Q2)
42.5000
Q125.75
Q358.75
IQR33.00
?How Do You Calculate Quartiles?
Quartiles divide data into four equal parts. Q1 (25th percentile) is the median of the lower half, Q2 (50th percentile) is the median, Q3 (75th percentile) is the median of the upper half. IQR = Q3 - Q1 measures spread. Outliers are typically values below Q1 - 1.5*IQR or above Q3 + 1.5*IQR.
What are Quartiles?
Quartiles are values that divide a data set into four equal parts. The first quartile (Q1) marks where 25% of data falls below, the second quartile (Q2 or median) marks 50%, and the third quartile (Q3) marks 75%. The Interquartile Range (IQR = Q3 - Q1) measures the spread of the middle 50% of data and is used for outlier detection.
Key Facts About Quartiles
- Q1 (first quartile) = 25th percentile, lower quartile
- Q2 (second quartile) = 50th percentile = median
- Q3 (third quartile) = 75th percentile, upper quartile
- IQR (Interquartile Range) = Q3 - Q1, measures middle 50% spread
- Five-number summary: Min, Q1, Q2 (Median), Q3, Max
- Lower fence = Q1 - 1.5 x IQR (values below are outliers)
- Upper fence = Q3 + 1.5 x IQR (values above are outliers)
- Box plots visualize quartiles with whiskers showing range
- Deciles divide data into 10 parts (D1-D9)
Try These Examples
Click an example to load sample data
Practice Quartile Problems
Test your understanding of quartiles and IQR
Practice with 4 problems to test your understanding.
Related Statistics Tools
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Quick Answer
Quartiles divide data into four equal parts. Q1 (25th percentile) is the median of the lower half, Q2 (50th percentile) is the median, Q3 (75th percentile) is the median of the upper half. IQR = Q3 - Q1 measures spread. Outliers are typically values below Q1 - 1.5*IQR or above Q3 + 1.5*IQR.
Frequently Asked Questions
Quartiles divide a sorted dataset into four equal parts. Q1 (first quartile) is the 25th percentile, Q2 (second quartile) is the median or 50th percentile, and Q3 (third quartile) is the 75th percentile.
IQR = Q3 - Q1. It measures the spread of the middle 50% of your data and is more robust to outliers than the full range. A smaller IQR indicates data is more tightly clustered around the median.
Using the IQR method: values below Q1 - 1.5*IQR (lower fence) or above Q3 + 1.5*IQR (upper fence) are considered outliers. Values beyond Q1 - 3*IQR or Q3 + 3*IQR are extreme outliers.
The five-number summary consists of: Minimum, Q1 (first quartile), Q2 (median), Q3 (third quartile), and Maximum. These five values provide a complete picture of data distribution and are used to create box plots.
A box plot (box-and-whisker plot) visualizes the five-number summary. The box spans Q1 to Q3 with a line at the median. Whiskers extend to min/max (or fences), and outliers are shown as individual points.
Deciles divide data into 10 equal parts (D1-D9). D1 = 10th percentile, D5 = 50th percentile (median), D9 = 90th percentile. Quartiles are special deciles: Q1=D2.5, Q2=D5, Q3=D7.5.
Last updated: 2025-01-15
How this works
Formulas follow standard definitions from the NIST Digital Library of Mathematical Functions and classical textbook derivations. Calculations run entirely in your browser. Where a closed-form solution exists, it is used; where an iterative or numerical method is required, the implementation is named on the page.
Sources
- [1]NIST Digital Library of Mathematical FunctionsAcademicdlmf.nist.govAccessed Apr 21, 2026
Joseph OrdunaFounder & Software Engineer
Full-stack software engineer specializing in embedded systems, web architecture, and AI/ML. Founder of Practical Web Tools. Built the gesture-controlled drone IP acquired by KD Interactive (Aura Drone, sold on Amazon).
Results
Median (Q2)
42.5000
50th percentile
Q1 (25th)25.7500
Q3 (75th)58.7500
IQR33.0000
Min12.00
Max120.00
Range108.00