Trips That Don't Fit the Box

A bike-share company is cleaning a column of trip durations, in minutes, before training a model to predict how long trips take. A few entries look wrong: a 2-minute trip that is probably someone re-docking a bike, a 240-minute trip from a bike that was never returned properly. Rather than judge them by eye, the team applies the standard IQR rule.

1. Quartiles. Sort the durations and split the sorted list into a lower half and an upper half. If the count is odd, the middle value (the median) goes into neither half. $Q_1$ is the median of the lower half and $Q_3$ is the median of the upper half. The median of an even-sized list is the average of its two middle values.
2. Fences. With $IQR = Q_3 - Q_1$:

1. Flag. A trip is an outlier if its duration is outside the fences: below the lower fence or above the upper fence. A duration exactly on a fence is kept.

Task: write iqr_fences(durations) and return a tuple (lower_fence, upper_fence, flagged):

• the two fences, each rounded to 4 decimal places;
• flagged, the positions of the outlier trips in the original durations list, in increasing order. If there are none, it's an empty list.

durations holds at least 4 numbers, in the order the trips were logged, not sorted.

The fences are built from $Q_1$ and $Q_3$, which one wild value barely moves. That's why this rule is often preferred over the z-score rule, whose mean and standard deviation get dragged around by the very outliers they are supposed to catch.