Box Plot Generator
Quartiles, median, whiskers, and outlier dots from a list of numbers.
Box Plot Generator
Create statistical box plots to visualize data quartiles, outliers, and distribution shape
Sample Datasets
How to read a box plot
Min, Q1, median, Q3, max—plus dots outside the whiskers
The box is the middle 50% of the data (Q1 to Q3). The line inside is the median. Whiskers reach the farthest points still inside the fences, usually Q1 − 1.5×IQR and Q3 + 1.5×IQR. Anything beyond those fences plots as an outlier.
- Min / Max: extremes of the sample (or whisker ends if outliers are pulled out)
- Q1 / Q3: 25th and 75th percentiles
- IQR: Q3 − Q1; fat box = more spread in the center
Median near Q1 with a long upper whisker usually means right skew. Median near Q3 with a long lower whisker usually means left skew. Centered median and even whiskers suggest something closer to symmetric.
Outliers and when they matter
Lower fence = Q1 − 1.5×IQR. Upper fence = Q3 + 1.5×IQR. That 1.5 rule is Tukey's convention, not a law of nature—use 3×IQR if you only want extreme flags.
Whiskers stop at the last in-fence point; they do not always hit the raw min/max. Flagged points can be typos, measurement glitches, or the most interesting cases in the set. Do not auto-delete them because the chart marked them.
Quick example: scores 1200, 1250, 1300, 1350, 1400, 1450, 1500, 1550, 1600 give a median around 1400 and IQR around 200. Compare that shape across classes or batches side by side—that is where box plots beat a single mean.
Frequently Asked Questions
Box plot or histogram?
Box plots for comparing groups in a small footprint. Histograms when you need the detailed shape of one distribution (peaks, gaps, multimodality).
Lots of outliers—bad data?
Maybe. Or heavy tails, mixed groups, or a threshold that is too tight. Check collection and consider a wider fence before blaming the data.
Median not centered in the box?
Skew. Closer to Q1 → right skew; closer to Q3 → left skew.
Compare groups with different n?
Yes, but note sample sizes. Tiny groups make quartile estimates jittery.
Show the mean too?
Useful. Mean far from the median usually means skew or a strong pull from extremes.
Minimum useful sample size?
You can draw one with five points; trust it more around 15–20+ per group.
Related Statistical Tools
Histogram Generator
See detailed distribution shape and frequencies.
Quartile Finder
Calculate Q1, Q2, Q3 and other percentiles.
Outlier Detector
Flag unusual values with IQR and Z-score rules.
Standard Deviation
Measure spread alongside the five-number summary.
Z-Score Calculator
Standardize values relative to the mean.
Correlation Analysis
Check relationships between variables.
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