IQR, point by point

The whole idea.
Sort the readings and find the two quartiles: Q1 & Q3. The gap between them is the interquartile range — the width of the middle half of your data:

IQR = Q3 − Q1    and a reading is odd if it falls below Q1 − m × IQR or above Q3 + m × IQR

Notice what is not in there: no mean, no standard deviation, no bell curve. Quartiles are positions in the sorted list, so moving one extreme reading further out does not move them at all. That single property is the whole reason this rule exists. m = 1.5 is Tukey's convention, and 3.0 is his “far out” fence.

Three things worth trying:
1. Bell, Many, fence 1.5. Twenty odd readings and all twenty are caught, with barely a false alarm. Now open the z-score page and set up the identical case: it catches about 7 of the 20. The difference is the whole lesson. A z-score measures against σ, which the outliers inflate; this rule measures against the quartiles, which they cannot budge. Watch the status line as you switch between None and Many: Q1 shifts by about 1 and Q3 by about 4, while on the z-score page the same twenty readings take σ from about 15 to 32.

2. Bell, Swamped, fence 1.5. Eighty odd readings out of 280 — nearly 29% of the data — and now IQR catches none of them either. The quartiles hold out until the bad points reach about a quarter of your data, and then they fall over too. Every rule on this page and the last one assumes the same thing: anomalies are rare. When they stop being rare, they stop being anomalies and become the distribution.

3. Skewed, None, fence 1.5. There is not a single odd reading here, yet 8 or so points are flagged, sample after sample — all of them in the long right tail, all of them perfectly ordinary for this shape. IQR is robust to outliers; it is not a cure for skew. A one-sided tail is normal for waiting times, incomes and file sizes, and this rule will complain about it every time. Raise the fence to 3.0 and the noise drops to about 2.