21.32 Safe margin of error. The margin of error is 0 when is 0 or 1 and is largest when is 1/2. To see this, calculate for = 0, 0.1, 0.2, . . . , 0.9, and 1. Plot your results vertically against the values of horizontally. Draw a curve through the points. You have made a graph of . Does the graph reach its highest point when ? You see that taking gives a margin of error that is always at least as large as needed.