The correlation of data contained in a series of signal sample values makes the estimation of the statistical characteristics describing such a random sample difficult. The positive correlation of data increases the arithmetic mean variance in relation to the series of uncorrelated results. If the normalized autocorrelation function of the positively correlated observations and their variance are known, then the effect of the correlation can be taken into consideration in the estimation process computationally. A significant hindrance to the assessment of the estimation process appears when the autocorrelation function is unknown. This study describes an application of the conditional averaging of the positively correlated data with the Gaussian distribution for the assessment of the correlation of an observation series, and the determination of the standard uncertainty of the arithmetic mean. The method presented here can be particularly useful for high values of correlation (when the value of the normalized autocorrelation function is higher than 0.5), and for the number of data higher than 50. In the paper the results of theoretical research are presented, as well as those of the selected experiments of the processing and analysis of physical signals.