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(statistics) An expression of the lack of precision in the results obtained from a sample.

Probability densities of polls of different sizes, each color-coded to its 95% confidence interval (below), margin of error (left), and sample size (right). Each interval reflects the range within which one may have 95% confidence that the true percentage may be found, given a reported percentage of 50%. The margin of error is half the confidence interval (also, the radius of the interval). The larger the sample, the smaller the margin of error. Also, the further from 50% the reported percentage, the smaller the margin of error.

(statistics) An expression of the lack of precision in the results obtained from a sample.

A visual representation of the Empirical (68-95-99.7) Rule based on the normal distribution.

(statistics) An expression of the lack of precision in the results obtained from a sample.

Log-log graphs of ${\displaystyle MOE_{\gamma }(0.5)}$ vs sample size n and confidence level γ. The arrows show that the maximum margin error for a sample size of 1000 is ±3.1% at 95% confidence level, and ±4.1% at 99%. The inset parabola ${\displaystyle \sigma _{p}^{2}=p-p^{2}}$ illustrates the relationship between ${\displaystyle \sigma _{p}^{2}}$ at ${\displaystyle p=0.71}$ and ${\displaystyle \sigma _{max}^{2}}$ at ${\displaystyle p=0.5}$. In the example, MOE₉₅(0.71) ≈ 0.9 × ±3.1% ≈ ±2.8%.