The deviations of six observations from their own mean are −5, 3, $x$, −2, 7 and −1. Find $x$.

Deviations measured from the mean always add up to exactly 0, because Σ$(x$ − mean) = Σ$x$ − n × mean = 0. The five known deviations give −5 + 3 − 2 + 7 − 1 = 2, so $x$ must be −2 to bring the total to zero. The value 2 is that running total with the sign left the wrong way round; 0 assumes the missing deviation must itself be nothing, which is only true when the observation happens to equal the mean; and −8 is the total of the negative deviations on their own.