Generate box-and-whisker plots with five-number summary, Tukey fences, outlier detection, percentile table, and Bowley skewness. Interactive SVG visualization.
The box plot calculator creates a box-and-whisker diagram from your data and pairs it with the summary statistics that explain what the plot is showing.
It computes the five-number summary, interquartile range, Tukey fences, mild and extreme outliers, and Bowley skewness, then renders the result as an SVG chart. You can switch between inclusive and exclusive quartile methods and adjust the fence multiplier when you want stricter or looser outlier cutoffs.
That makes the page useful both for quick exploratory analysis and for checking the exact fence values behind a box plot before you reuse the chart in notes, teaching material, or reports.
Box plots are the single best tool for quickly summarizing data distribution. This calculator gives you the complete picture: five-number summary, Tukey fences, outlier identification, skewness measurement, and a ready-to-use SVG visualization.
Whether you're comparing groups, screening for outliers, or presenting data summaries, the box plot calculator delivers every metric you need alongside the visual representation.
IQR = Q3 − Q1. Lower fence = Q1 − k × IQR. Upper fence = Q3 + k × IQR. Standard: k = 1.5 (mild), k = 3 (extreme). Bowley skewness = (Q3 + Q1 − 2 × Median) / IQR.
Result: Min=68, Q1=73, Median=82.5, Q3=89, Max=95, IQR=16, No outliers
The 12 test scores have a median of 82.5 with an IQR of 16. All values fall within the fences (Q1 − 1.5×IQR = 49, Q3 + 1.5×IQR = 113), so there are no outliers. The box plot shows a slight left skew.
The box plot was invented by John Tukey in 1970 as part of exploratory data analysis (EDA). The "box" spans Q1 to Q3, capturing the middle 50% (the interquartile range). The median line inside the box shows central tendency. Whiskers extend to the most extreme values within the fences, and outliers appear as individual points beyond the whiskers.
A symmetric box plot has the median centered in the box with equal-length whiskers. A right-skewed plot has the median closer to Q1, with a longer right whisker and upper outliers. A left-skewed plot is the mirror image. The relative lengths of whiskers and position of the median tell you about data asymmetry at a glance.
Modern alternatives like violin plots combine box plots with kernel density estimates, showing the full distribution shape. However, box plots remain preferred for their simplicity and interpretability, especially when comparing many groups. They clearly show outliers, which violin plots often obscure.
Last updated:
This calculator parses the submitted values, sorts them, and computes the five-number summary directly from the dataset. Quartiles follow the selected convention: the inclusive method keeps the median in both halves for odd-sized datasets, while the exclusive method removes it from both halves before computing Q1 and Q3.
The interquartile range is computed as Q3 − Q1. Tukey fences are then calculated as Q1 − k × IQR and Q3 + k × IQR, where k is the user-selected fence multiplier. Whiskers extend to the most extreme non-outlier observations inside those fences, and Bowley skewness is reported as (Q3 + Q1 − 2 × median) / IQR.
Percentiles in the summary table use linear interpolation between adjacent ordered values. Values shown in the UI are rounded for display only.
A box plot shows the five-number summary: minimum, Q1 (25th percentile), median (50th percentile), Q3 (75th percentile), and maximum. The box spans Q1 to Q3 (the IQR, containing the middle 50% of data). Whiskers extend to the most extreme non-outlier values. Outliers are shown as individual points.
Values beyond the "fences" are outliers. The standard (Tukey) fences are Q1 − 1.5×IQR and Q3 + 1.5×IQR. Values beyond these are "mild outliers." Values beyond Q1 − 3×IQR or Q3 + 3×IQR are "extreme outliers." These thresholds were chosen by John Tukey because they work well for normally distributed data.
The inclusive method includes the median in both the lower and upper halves of the data (used in many textbooks). The exclusive method excludes the median from both halves. Results differ most for odd-sized datasets. The difference is usually small, but be consistent in your analysis.
Box plots are better for comparing multiple groups, showing outliers, and displaying data compactly. Histograms are better for showing the detailed shape of a single distribution (bimodality, gaps). Use box plots for comparison and histograms for detailed distribution analysis.
Bowley skewness (quartile skewness) measures symmetry using quartiles: (Q3 + Q1 − 2×Median) / IQR. It ranges from −1 to +1. Zero means perfectly symmetric quartiles. Unlike Pearson's skewness, it's robust to outliers since it only uses quartiles.
You need at least 5 values to compute the five-number summary. However, box plots become more meaningful with 20+ data points. With fewer than 10 values, individual data displays (dot plots, stem-and-leaf plots) may be more informative.