Stationary tests to find mean values are common in testing; e.g. when measuring the resistance force of a model ship in a towing tank facility. Literature involving uncertainty analysis often suggest that quantifying the random scatter of mean should be done by performing repeat tests. However, this may be expensive and time consuming. This paper presents an estimator to quantify the Random Uncertainty of the Mean (RUM) from a stationary single time series, without performing actual repeat tests. The numerical implementation of this estimator is provided as well. Further, this paper presents two other methods, one to qualify the stationarity, and one to quantify spectral contributions to the random uncertainty. The presented estimator and methods are based on the auto-covariance of a time series and are valid for certain classes of random signals. These classes are typical for time series measured in stationary tests. For these classes RUM has been validated with the analytical solution for the random uncertainty of mean. To check for stationarity of time series data, a pragmatic method has been developed, the Transient Scanning Technique (TST). The TST objectively identifies and deletes start and end effects in measurements. It detects instationarities which wouldn’t be detected by visual inspection of the time series data. A by-product of a RUM calculation is a spectral distribution of the uncertainty contributions to the random uncertainty of mean. This method is called the Uncertainty Spectrum Technique (UST). The RUM, TST and UST are demonstrated with a set of flat plate measurements.