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 a five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. Invented by statistician John Tukey, it is one of the most widely used tools in exploratory data analysis.
The "box" spans from Q1 to Q3 — the interquartile range (IQR) — and contains a line marking the median. The "whiskers" extend to the most extreme data points within 1.5 × IQR of the quartiles. Points beyond the whiskers are plotted individually as potential outliers.
This free box plot maker runs entirely in your browser: paste your numbers and the box and whisker plot maker online computes every five-number summary locally — nothing is uploaded and no account is needed. It works as a box plot maker with outliers flagged automatically by the Tukey fences, as a box plot maker with 5 number summary tables for every dataset, and as a modified box plot maker in the classic Tukey sense, where whiskers stop at the fences and extreme points are drawn individually.
Add a second dataset and it becomes a double box plot maker for two-group comparison; add up to ten and you have a parallel box plot maker for side-by-side groups. It also doubles as a box plot maker for Excel data — copy any spreadsheet column and paste it directly, no add-in or export step required.
Why Use Box Plots?
- Compare groups instantly. Place boxes side by side to see medians, spreads, and outliers across categories.
- Detect skewness visually. A lopsided box reveals asymmetry — long upper whisker = right skew.
- Identify outliers objectively. The IQR-based Tukey fences method flags statistically unusual data points.
- Summarize large datasets compactly. One box plot can represent thousands of data points.
Worked Example: Computing a Box Plot by Hand
Take a small dataset of 10 test scores: 52, 58, 63, 67, 71, 74, 78, 82, 85, 88. Step 1 — sort (already sorted here). Step 2 — the median is the average of the 5th and 6th values: (71 + 74) / 2 = 72.5. Step 3 — split at the median; the lower half is 52, 58, 63, 67, 71, whose middle value is Q1 = 63; the upper half is 74, 78, 82, 85, 88, whose middle value is Q3 = 82.
Step 4 — compute the IQR: 82 − 63 = 19. Step 5 — the Tukey fences are 63 − 1.5×19 = 34.5 (lower) and 82 + 1.5×19 = 110.5 (upper). Every value lies inside the fences, so the whiskers simply reach the true extremes: min = 52, max = 88, and there are no outlier dots.
Paste those same ten numbers into the tool and compare: the box runs from 63 to 82, the median line sits at 72.5 — slightly left of center inside the box, a gentle hint of right skew. Doing this by hand once makes every box plot you meet afterward instantly readable.
Common Misreadings
- Reading the box width as sample size. A wide box means high variability in the middle 50%, not more data points.
- Assuming symmetry inside the box. A box plot cannot show bimodality — two clusters can hide in one box. Cross-check with a violin plot.
- Treating whiskers as min/max in all tools. Tukey-style whiskers stop at the fences; true extremes beyond them appear as outlier dots.
- Comparing medians without spread. Two groups can share a median while one is twice as variable — always read the IQR together with the median.
Related Tools
Frequently Asked Questions
Is there a free box plot maker online?
What does a box plot show?
How many data points do I need?
Can I compare multiple datasets?
How are outliers detected?
Key Terms
- Minimum (Min)
- The smallest data point excluding outliers.
- First Quartile (Q1)
- The median of the lower half. 25% of data falls below Q1.
- Median (Q2)
- The middle value. 50% of data falls below the median.
- Third Quartile (Q3)
- The median of the upper half. 75% of data falls below Q3.
- Maximum (Max)
- The largest data point excluding outliers.
- Interquartile Range
- Q3 − Q1. Measures statistical spread; the width of the box.
- Mean
- The arithmetic average of all data points.
- Outliers
- Data points below Q1−1.5×IQR or above Q3+1.5×IQR (Tukey fences).
Computation Method
- Quartiles are calculated using linear interpolation (method 7 from Hyndman & Fan, 1996), consistent with Python's NumPy and pandas defaults.
- Outlier detection uses the Tukey fences method: lower fence = Q1 − 1.5 × IQR, upper fence = Q3 + 1.5 × IQR.
- Chart scaling caps the display axis at the upper fence value so the visualization remains clear even when extreme outliers are present.
References
- Tukey, J. W. (1977). Exploratory Data Analysis. Addison-Wesley.
- McGill, R., Tukey, J. W. & Larsen, W. A. (1978). "Variations of Box Plots." The American Statistician, 32(1), 12–16.
- Frigge, M., Hoaglin, D. C. & Iglewicz, B. (1989). "Some Implementations of the Boxplot." The American Statistician, 43(1), 50–54.
- Hyndman, R. J. & Fan, Y. (1996). "Sample Quantiles in Statistical Packages." The American Statistician, 50(4), 361–365.