  We study the influence of measured high cumulants of conserved charges on
their associated statistical uncertainties in relativistic heavy-ion
collisions. With a given number of events, the measured cumulants randomly
fluctuate with an approximately normal distribution, while the estimated
statistical uncertainties are found to be correlated with corresponding values
of the obtained cumulants. Generally, with a given number of events, the larger
the cumulants we measure, the larger the statistical uncertainties that are
estimated. The error-weighted averaged cumulants are dependent on statistics.
Despite this effect, however, it is found that the three sigma rule of thumb is
still applicable when the statistics are above one million.
