Free · Descriptive statistics calculators 📊

Relative Standard Error as a Percentage of the Mean

Compare a supplied standard error with the magnitude of a nonzero mean, retaining a nonnegative relative percentage.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A mean of −100 with standard error 5 has relative standard error 5/|−100| × 100 = 5%.

Relative standard error = standard error / |mean| × 100%

Worked example

Enter these known values and leave the other values blank.

Estimated mean, nonzero: -100
Standard error of the mean: 5

Relative standard-error magnitude: 5 %

Assumptions and limitations

Standard error and relative standard error are nonnegative. The mean is nonzero and may be negative.
Use the supplied standard error, not the standard deviation of individual observations. The calculator does not estimate a standard error from a sample or a survey design.
The inverse mean returns the positive magnitude. Relative error alone cannot recover its sign; zero standard error with zero relative error cannot identify a mean.
This ratio is sensitive to means near zero and is meaningful only for a suitable measurement scale with a meaningful zero. It does not measure bias or total accuracy.

Common questions

Why is the answer positive for a negative mean?

This tool reports the magnitude convention, dividing by the absolute value of the mean. The sign of a mean is not a sign of uncertainty.

Is a small relative standard error proof of an accurate estimate?

No. It describes supplied sampling variability relative to the estimate’s size. Bias and other error sources can still be present.

References

Bookify defines relative standard error as a nonnegative magnitude using the absolute mean; the inverse mean chooses the positive branch. Bookify rejects a zero mean and negative relative standard error.

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