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

In this formula, z represents the z-value of a certain confidence level, s is the standard deviation of the sample, and n 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 z — 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 x to find the bounds of a confidence interval.