Just wondered . I assume you checked what your scope was reading without a connection.
As there is a natural floor noise . etc . I guess you did . and minus the difference
My scope has about 650uv of static floor. (scopes voltages are not always that accurate on volts).
setting @ 1mv
TB @ 2ns
when adding the 962 set to DC volts setting @ 0v (scope)
DC volts setting @ 10v 1.312mv (scope)
scope read 0v 107uv AC coupling . (edit typo)
scope Ac 800uv vRMS peek det. minus floor 267uv = 533uv Vrms
also tried on my bench meter set for AC/DC showed 0.008 v on 0v & 10v (962 setting)
The bench meter has Isolated inputs RG connector so it would not act as a ground for the 962
The test was done with the supplied UNI-T Power SMPS unit . No added grounding.
I reckon that's not bad there is some noise but on my HP CRT it was showing interference
RF from some where .
When a ground was added did remove some of the stray RF etc .
There are too many unknowns as everyone lives in different locations different mains layouts .
Lighting , wife's hair drier ,wifi and so on etc . Police tx are the worst ,
My home lab has good sockets connection and I tested the connections etc.
Led lighting is also noisy .
For a cheap setup I don't think much improvement is required .
Faraday Cage .. Last resort if I get paranoid