For a set of 8 observations the sum of the deviations of the observations from 30 is 20. What is the mean of the observations?

Σ$(x-30)$ = Σ$x-8\times 30=20$, so Σ$x=240+20=260$ and the mean is 260 ÷ 8 = 32.5. Answering 2.5 stops at 20 ÷ 8 and never puts the 30 back; 27.5 subtracts it instead of adding it; and 30 assumes the deviations were measured from the mean, which is the one value about which they always add up to 0.