Ok I know that Var[X] = E[(X-E[X])^2]. But I just can't help but think that the variance should always be zero. I think it makes so much sense, but obviously the formula says otherwise... But look, my reasoning seems so perfect: 1) The variance is the expected difference from the mean, squared 2) The expected value of X is the mean 3) So shouldn't we always expect X to be the mean, and so (X - mean)^2 = 0^2 = 0? But obviously it doesn't work out that way....it's so weird. Does anyone know an intuitive reason why Var[X] shouldn't be zero? What's wrong with my logic?