A bottling plant outside Tashkent fills half-litre bottles of apple juice. No machine fills every bottle to exactly 500 millilitres, so the plant works with a tolerance: every bottle must be within 4 millilitres of 500. In other words, the error may be no more than 4 millilitres in either direction.
That rule describes a range with a centre. The lowest acceptable bottle holds 496 millilitres and the highest holds 504. A bottle of 496 is fine; a bottle of 495 is not. A bottle of 504 is fine; a bottle of 505 is not.
Every hour, the quality inspector, Farrux, takes five bottles from the line and measures them. On Tuesday morning the five readings were 497, 503, 505, 495 and 501. He did not compare each number with two limits. He asked one question instead: how far is this bottle from 500? The answers were 3, 3, 5, 5 and 1. Two bottles were more than 4 away, so two of the five were rejected.
Two failures in five is far too many, so Farrux stopped the line. The problem was a worn valve that sometimes let too much juice through and sometimes too little. Notice that one bad bottle was over the limit and one was under it: the machine was not filling too much or too little, it was filling unevenly.
After the valve was replaced, the next sample read 499, 502, 500, 498 and 501. Every bottle was within 2 millilitres of the target, well inside the tolerance, and the line started again.