An outlier is a value far enough from the rest that it deserves a second look — not automatically an error, and never automatically deleted. John Tukey's rule builds two cutoffs out of the box plot you already have: $LF = Q_1 - 1.5\,IQR$ and $UF = Q_3 + 1.5\,IQR$. Read aloud: lower fence equals Q-one minus one-point-five I-Q-R. $LF$ is the lower fence and $UF$ the upper fence, both in the data's own unit; $Q_1$ and $Q_3$ are the first and third quartiles; $IQR = Q_3 - Q_1$ is the box's width, which you must build FIRST. Anything outside a fence is flagged.

Two things about the 1.5. It is a convention, chosen by Tukey because on normal data it flags roughly the most extreme 1 in 150 — rare enough to be interesting, common enough to be worth checking. And it is exact: 1.5, not 1, not 2. The other quiet fact is that this rule never consults the mean or the standard deviation. It is built from quartiles alone, which is precisely why it survives skewed data that would drag a mean off its feet.

A fence is a BOUNDARY, not an observation — the data need not contain a value anywhere near it. And the question a fence answers is a decision, so finish the decision: compute the fence, compare the suspect reading with it, and say flag or leave. A fence with no verdict attached is half an answer.