Box Plot Calculator
Paste numeric data to instantly generate the five-number summary, interquartile range (IQR), and potential outlier fences.
Five-number Summary
Minimum: 1.000
Q1: 3.250
Median: 5.500
Q3: 7.750
Maximum: 10.000
Count: 10
Mean: 5.500 • Interquartile Range (IQR): 4.500
Lower Fence: -3.500 • Upper Fence: 14.500
Observations below the lower fence or above the upper fence are potential outliers in a box plot.
How to Use This Calculator
- Paste your dataset (numbers only) into the input box.
- Review the five-number summary and IQR for box-and-whisker plots.
- Use the fences to flag observations that may warrant outlier review.
- Export or screenshot results for reporting or further analysis.
Formula
Median (Q2) = middle value or average of two middle values.
Q1 = 25th percentile • Q3 = 75th percentile.
IQR = Q3 − Q1.
Lower Fence = Q1 − 1.5 × IQR • Upper Fence = Q3 + 1.5 × IQR.
Box plots summarize distribution shape, central location, and dispersion, making them useful for comparing datasets or detecting outliers.
Frequently Asked Questions
What is the five-number summary?
It consists of the minimum, Q1, median, Q3, and maximum. These anchor box plot elements.
How are quartiles computed?
This calculator interpolates quartiles using the (n − 1) × q formula, consistent with many statistical packages.
Why use fences and not absolute cutoffs?
Fences offer a rule-of-thumb for outlier detection based on distribution spread rather than arbitrary thresholds.
Can I visualize the box plot?
This calculator delivers numeric summary values. Use them in charting tools or statistical software to draw the plot.