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Maximum Error of Estimate

The maximum error of estimate, also known as the margin of error, is the maximum difference between the estimate of the population mean and its actual value. The maximum error of estimate is calculated using the following formula.

In this formula, represents the value of a certain confidence level, is the standard deviation of the sample, and is the sample size. From the formula, some conclusions can be made about the error of estimate.

  • Increasing the sample size while the standard deviation remains the same will result in a smaller margin of error.
  • Conversely, an increase in the standard deviation while the sample size remains the same will cause a bigger margin of error.
  • The greater the absolute value of — meaning an increase in the confidence level — the greater the margin of error.

The maximum error of estimate is added to and subtracted from the estimation mean to find the bounds of a confidence interval.

Grafical Representation of the Maximum Error of Estimate in Confidence Intervals