Percentiles, the IQR and the 1.5 Outlier Rule: How to Flag a Bad Row
By Michael Nocito , data analyst · Published August 9, 2026 By the end of this page you can compute quartiles by hand, build the standard outlier fence from them, and run that fence over any column to get back a short list of rows worth looking at. On the sixteen orders below, one mistyped quantity gets flagged automatically while every honest large order stays inside the fence. Here is what to actually do today. On the column you care about most, get four numbers: the 25th percentile, the 75th, their difference, and 1.5 times that difference added to the 75th. Anything above that last number is a row to open and read. It is one query, and it turns "is this data clean" into a list of specific rows. The short version: a percentile is a value with a known share of the data below it. The interquartile range is the width of the middle half. Values more than one and a half of those widths beyond the middle half get flagged. The fence is easier to see than to read, so it gets the picture. The original carries a diagram here. In words: A horizontal line with a row of small filled dots along it, spaced unevenly and thinning out towards the right. A tall rectangle is drawn around the dots in the middle of the row, covering the central half of them, with a thick vertical bar inside it. The rectangle's left edge is labelled Q1, its right edge Q3, and the bar inside it median. From each edge of the rectangle a horizontal whisker line runs outward to a short vertical cap, reaching the furthest dot on that side that still lies within range. To the right of the right-hand cap stands a tall dashed vertical line labelled fence, drawn one and a half rectangle-widths beyond the rectangle's right edge, with a small double-headed measuring arrow underneath showing that distance against the rectangle's own width. One lone dot sits well to the right of that dashed line, drawn as a hollow ring instead of a filled dot, so it reads as picked out rather than belonging with the rest. Every oth