Box Plot Calculator
A Box Plot Calculator quickly computes the 5-number summary (Min, Q1, Median, Q3, Max) and identifies statistical outliers using the 1.5x Interquartile Range rule.
Updated December 2025
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Comma, space, or newline separated. n = 14
Min
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Q1
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Median
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Q3
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Max
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IQR
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Spread
Sample Dataset
5-Number Summary
Box Plot Analysis Guide
A comprehensive interactive suite for interpreting Distributions. Understand whiskers, identify outliers, and master the 5-number summary.
The Outlier Test Bench
At what point does a data point become an "Outlier"? Drag the slider below to test the 1.5x IQR Rule.
Value: 480 (Normal Range)
Reading Your Data
Don't just look at the median. The length of the whiskers and the position of the box tell you the story of your data's quality.
Normal
Symmetric (Bell Curve)
The whiskers are equal length. The median is in the middle. This is the ideal state for most processes.
Predictable & Stable Skewed
Skewed (Lopsided)
One whisker is much longer than the other. The median is pushed to one side. Indicates a natural limit (like 0) or a process drift.
Action: Investigate Tail Issues
Heavy Outliers
Dots appearing beyond the whiskers. These are data points statistically far from the norm (1.5x IQR).
Action: Root Cause Analysis Data Health Hover over list to test
Anatomy of the Box
The "Box" isn't random. It represents the Middle 50% of your data. This is where the majority of your process lives.
The Box (IQR)
Interquartile Range
The distance between Q1 (25%) and Q3 (75%). A short box means your data is consistent. A tall box means high variation.
The Whiskers
The Range (Non-Outlier)
These lines extend to the furthest data points that are not outliers. They show the full spread of "normal" variation.
The Box contains the middle 50% of all data points.
[Image of normal distribution vs box plot]
Why not use Mean?
The Box Plot uses the Median because averages are easily corrupted by outliers. If Bill Gates walks into a bar, the "average" wealth skyrockets, but the "median" wealth stays the same.
The Formulas
How do we decide what is an "Outlier"? We use Tukey's Rule.
The Range
IQR Formula
IQR= Q3-Q1
Simply subtract the 25th percentile value from the 75th percentile value. This represents the height of your box.
The Boundaries
Outlier Fence
Fence= Q3+ (1.5 × IQR)
Any data point that sits 1.5 times the height of the box away from the box is statistically considered an outlier.
Troubleshooting Distributions
Scenario A
Too Many Outliers
Symptom: Dots appear above/below the whiskers.
Data Entry Error
Did someone type "100" instead of "10"? Check the raw data first.
Mixed Processes
Are you combining data from Machine A and Machine B? If they run differently, the combined data will look messy.
Scenario B
Extreme Skew
Symptom: Median line is stuck to the top or bottom.
Natural Limits
Is your data close to Zero? (e.g. Flatness or Runout). You can't be less than 0, so data piles up there.
Process Drift
The tool might be wearing out, causing values to slowly drift in one direction over time.
Expert Knowledge
Common Questions
Should I delete outliers?
Generally, No. Outliers are often the most valuable part of your data—they tell you when something went wrong. Only delete them if you can prove they are measurement errors (e.g., a typo).
Why is the median line not in the center?
This indicates Skewness. If the median is closer to the bottom of the box, your data is "Positively Skewed" (most data is low, with a tail of high values). If it's closer to the top, it is "Negatively Skewed".
Verified Expert
Disclaimer: This tool is for informational and educational purposes only. Calculations are based on standard formulas but may not account for unique business variables. We do not accept liability for decisions made based on these results.