Box Plot

There are at least nine definitions of a sample quartile, and on small groups they give visibly different boxes. A chart that silently uses one definition while your measures use another will disagree with your own numbers. SmartVisuals Box Plot defaults to the definition behind Excel and DAX PERCENTILE.INC and QUARTILE.INC, so the box agrees with the model.

The exclusive definition (PERCENTILE.EXC), Tukey's hinges and all nine Hyndman-Fan types are one setting away, and the footnote always names the one in use. Reference lines for the mean, the median and up to four percentiles use the same method, so a P25 line sits exactly on the lower hinge. A typed reference line, such as a target, can be added on top.

Four whisker rules are free: 1.5 x IQR with any multiple, percentiles, mean +/- SD, and minimum to maximum. With the IQR, percentile and SD rules, whiskers end on the most extreme observation inside the fences, and everything outside is an outlier.

Outliers are drawn as hollow triangles and far outliers, beyond 3 x IQR from the box, as filled triangles. No theme draws ordinary points as triangles, so an outlier reads by shape and never by colour alone. Behind each box a beeswarm, jitter or strip shows every observation; hover a point for its ID and click it to filter the rest of the report to that unit (for boxes of up to 2,500 points; larger boxes draw their points as one image).

Power BI sends up to 30,000 rows per window, and the visual fetches further windows up to 150,000 rows, with the host's warning icon when the data reaches the cap. For larger tables, put the value itself in Value (as column) with a Count measure: each distinct value arrives once and is expanded inside the visual, so a million observations can arrive as a few thousand rows and the quartiles are identical to row input.

Split By a second field for side-by-side boxes, for example shifts within each line, sort groups by median, mean, spread or n, hide groups below a minimum size, draw the boxes horizontally or vertically, and switch to a logarithmic scale for skewed values.

Two boxes that look apart may still be noise. Premium adds significance between groups: Welch t or Mann-Whitney U tests, adjusted with Holm or Bonferroni, and an overall Welch's ANOVA, one-way ANOVA or Kruskal-Wallis test, drawn as brackets with stars or as A / B / C letters. Notched boxes and mean confidence intervals show the uncertainty around each median and mean.

Premium also adds a Weight field for survey and sampling weights (weighted quartiles, means and Welch tests with the Kish effective sample size), spec limits typed or from measures with Cp, Cpk, Cpl, Cpu, Cpm, Pp and Ppk per group, and small multiples. Every statistic is golden-tested against independent reference implementations, and degenerate cases show n/a, never a false result.