HP 54710A User's Reference Manual page 213

Measurements
Statistics
If the standard deviation of the oscilloscope's jitter is 1/3 of the standard
deviation of the actual jitter, the error in the measured standard deviation
will be about 5 percent.
Jitter and Averaging
Vertical averaging removes the apparent jitter on the display, but may give
misleading information about the true behavior of the signal. For example,
consider measuring rise time. Figure 13-12 shows a rise time measurement
on a jittering signal with averaging turned on.
Figure 13–12
Erroneous Rise Time Measurements Due to Jitter
13–28