A raw value says little on its own, because 50 is extreme for delivery minutes and ordinary for exam marks.
The z-score rescales any value into standard deviations from the mean, so values from different columns become comparable.
That shared scale is what makes a single cut-off, such as 3, usable across many columns.
The steps are to work out the mean and the standard deviation, then subtract the mean from each value and divide.
A value equal to the mean has a z-score of 0, and values below the mean get negative scores.
If data follows a normal distribution, about 99.7% of values fall within 3 standard deviations of the mean.
So a z-score beyond 3 should appear only about 3 times in every 1,000 values from a normal distribution.
In a table of 1 million rows, that still means around 2,700 flags even when nothing is wrong.
The cut-off can be raised for large tables or lowered for small ones, depending on how many flags are useful.
The method has a weakness called masking: a few huge values raise the standard deviation and hide each other.
In a column of 10 values or fewer, no value can score above 3 at all, however extreme it is.
Robust versions replace the mean with the median and the standard deviation with a spread measure that ignores extremes.
In practice z-scores suit roughly bell-shaped measurements, such as sensor readings or test marks.
For skewed columns, taking logarithms first can make the shape closer to a bell before scoring.
The usual mistake is removing everything beyond 3 automatically, when the cut-off only says where to look.