Editing Margin of error (section)

== Specific margins of error ==

If a poll has multiple percentage results (for example, a poll measuring a single multiple-choice preference), the result closest to 50% will have the highest margin of error. Typically, it is this number that is reported as the margin of error for the entire poll. Imagine poll <math>P</math> reports <math>p_{a},p_{b},p_{c}</math> as <math>71%, 27%, 2%, n=1013</math>

:<math>MOE_{95}(P_{a}) = z_{0.95}\sigma_\overline{p_{a}} \approx 1.96\sqrt{\frac{p_{a}(1-p_{a})}{n}} = 0.89/\sqrt{n}=\plusmn2.8%</math> (as in the figure above)

:<math>MOE_{95}(P_{b}) = z_{0.95}\sigma_\overline{p_{b}} \approx 1.96\sqrt{\frac{p_{b}(1-p_{b})}{n}} = 0.87/\sqrt{n}=\plusmn2.7%</math>

:<math>MOE_{95}(P_{c}) = z_{0.95}\sigma_\overline{p_{c}} \approx 1.96\sqrt{\frac{p_{c}(1-p_{c})}{n}} = 0.27/\sqrt{n}=\plusmn0.8%</math>

As a given percentage approaches the extremes of 0% or 100%, its margin of error approaches ±0%.