Box Plot Generator
Generate a box and whisker plot for your data with ease. This calculator computes the five-number summary (minimum, Q1, median, Q3, maximum), the interquartile range (IQR), detects outliers using Tukey's fences (1.5 × IQR), and visualizes the distribution with an interactive box plot.
What Is a Box Plot?
A box plot (also called a box-and-whisker plot) is a standardized way of displaying the distribution of data based on the five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. It was invented by the American statistician John Tukey in the 1970s.
Anatomy of a Box Plot
- Box: Spans the interquartile range (IQR = Q3 − Q1), containing the middle 50% of the data.
- Median Line: A line inside the box marking the median (Q2).
- Whiskers: Lines extending from the box to the most extreme non-outlier values.
- Outliers: Points beyond the whiskers, plotted individually.
The Five-Number Summary
Every box plot is built on five key values:
- Minimum: The smallest value that is not an outlier.
- Q1 (First Quartile): The 25th percentile , 25% of data falls below this value.
- Median (Q2): The 50th percentile , the middle value.
- Q3 (Third Quartile): The 75th percentile , 75% of data falls below this value.
- Maximum: The largest value that is not an outlier.
Plus the Interquartile Range (IQR) = Q3 − Q1, which measures the spread of the middle 50% and is used to detect outliers.
Outlier Detection with Tukey's Fences
John Tukey's fences method is the industry standard for detecting outliers:
- Lower Fence: Q1 − 1.5 × IQR
- Upper Fence: Q3 + 1.5 × IQR
- Any value outside these fences is flagged as an outlier.
Why Use This Box Plot Generator?
- Complete Analysis: Get the five-number summary, IQR, and outlier detection.
- Interactive Chart: Visualize your data distribution with a professional box plot.
- Flexible Data Entry: Add numbers individually or paste entire datasets.
- Free & Private: No registration, no data storage.
❓ Box Plot Generator FAQ
What is a box plot?
A box plot (box-and-whisker plot) is a graphical representation of data that shows the distribution through quartiles, median, and outliers. It was invented by John Tukey in the 1970s.
What is the five-number summary?
The five-number summary consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. These five values form the basis of a box plot.
What is the interquartile range (IQR)?
The IQR is the difference between the third quartile (Q3) and the first quartile (Q1): IQR = Q3 − Q1. It represents the spread of the middle 50% of the data.
How are outliers detected in a box plot?
Outliers are detected using Tukey's fences method: values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are flagged as outliers.
What are the whiskers in a box plot?
The whiskers extend from the box to the most extreme data points that are not outliers. They show the range of the data excluding outliers.
What does a box plot tell me about my data?
A box plot shows the center (median), spread (IQR), skewness (by the position of the median within the box), and outliers of your data distribution.
How does this calculator compute quartiles?
This calculator uses linear interpolation (method 7), which is the default in Python's NumPy and pandas. This method provides the most accurate quartile estimates.
Can I adjust the IQR multiplier for outlier detection?
Yes! The default is 1.5 (Tukey's fences), but you can change it to 3.0 in the controls to detect only extreme outliers.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required. All calculations are performed in your browser.