But we have a margin of plus or minus 3 percentage points. What that means is if we kept taking samples, 95 percent of the time, we’ll get an estimate in that range of 46 to 52 percent.

Conversely, larger samples can reduce the margin of error, improving the precision of the measure. More on polls: How to tell if a political poll is skewed.

A version of this article appears in print on , Section A, Page 2 of the New York edition with the headline: Where Polls Can Mess Up (and How to Fix It). Order Reprints | Today’s Paper | Subscribe ...