Paste your data and instantly visualise the five-number summary, IQR, whiskers, and outliers — with a real box plot chart and plain-English interpretation of distribution shape.
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Paste your data and press Calculate to see the five-number summary, IQR, outliers, and a real box plot chart.
15 call handling times, one outlier hiding in the data. Enter the lab and visualise the spread — find the outlier and the true centre.
Use the calculator above to paste your data and instantly visualise the five-number summary, inter-quartile range, whiskers and outliers on a real box plot, with plain-English interpretation of distribution shape. The box plot is the fastest way to see whether data is symmetric, skewed or contaminated by outliers.
A box plot (or box-and-whisker plot) is a graphical summary of a data set using the median, the lower and upper quartiles, and whiskers that extend to the most extreme non-outlier values. Outliers are plotted as individual points. It is one of the most information-dense visualisations in statistics.
The five-number summary is: minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), maximum. The box spans Q1 to Q3 (the inter-quartile range, IQR). Whiskers extend to the most extreme values within 1.5 × IQR from the box. Anything beyond that is plotted as an outlier.
Two operators produce parts with the same average weight (50g) but very different distributions. Operator A: box from 49.8 to 50.2, no outliers — tight, controlled. Operator B: box from 49.5 to 50.5, with three outliers above 51 — wider variation, evidence of occasional special causes.
The box plots tell the story instantly: averages are identical, but Operator B is far more variable and has out-of-control episodes. Mean alone would have hidden both signals. That is why a box plot belongs alongside every summary statistic in process analysis.
Box plots expose distribution shape, spread and outliers in seconds. They are essential for spotting skewed data, comparing groups, and seeing whether averages are honest representations of the underlying data.
Use box plots whenever you want to compare distributions — between operators, shifts, suppliers, products, or time periods. They are essential at the Measure and Analyse phases of DMAIC.
Box plots sit alongside histograms, Pareto charts and control charts as core SPC visualisations. They are particularly useful for detecting non-normality before applying capability indices or t-tests.
When a box plot shows skew, transform the data or use non-parametric tests. When it shows outliers, investigate them — they are often the source of process knowledge, not just nuisance. When it shows wide IQR, run a variation-reduction project.
Pair box plots with histograms, control charts and hypothesis tests for a complete distribution-analysis toolkit.
A graphical summary of a data set showing the minimum, lower quartile, median, upper quartile and maximum, with outliers plotted as individual points.
The IQR is the distance from Q1 (25th percentile) to Q3 (75th percentile) — the box itself. It captures the middle 50% of the data and is robust to outliers.
Conventionally, any point further than 1.5 × IQR from the nearest end of the box. Some teams use 3 × IQR for "extreme outliers".
Use a box plot for compact group comparisons (multiple distributions side-by-side). Use a histogram when shape detail matters more than comparison.
Yes — they make no normality assumption, which is one of their main strengths. They are particularly useful for detecting non-normality before further analysis.
Want to use box plots as part of structured data analysis in an improvement project? The Green Belt covers this in full.
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