I have a handheld rechargeable Measuring Instrument. When I use it normally, without charger connected, readings on screen are stable. But when I connect the charger into it (It's a 5V USB charger) the readings jump around by 10 to 15 counts. So Why is this happening and it gets worse if I move my hand around it.
This is undoubtedly all to do with the quality of the charger, as well, possibly your hands.
You see, what a cheap 5V supply does (which is 99.9999999% of all USB chargers), is make a "floating-ish" voltage, which has only a very weak relevance to power earth. If at all. If it is a simple 2 prong adapter it may even relate the signal to one of those prongs through a tiny capacitor, effectively making it wobble up and down at the rated frequency (50Hz or 60Hz usually) compared to Power Earth, if it happens to be plugged so that it related to the phase.***
Add to that introduced switching noise of the adapter itself, and you've got yourself a horribly noisy 5V.
You see, the device's point of view is "I am stable at 5V", if that 5V then flaps up and down compared to the world around it, you may say "Whaaah, this supply voltage is unstable!", because you can say that with your "bird's eye view" of the situation. But the device still sees a "nice" 5V, but from its view of the world, the entire world around it now flops up and down 50 to 60 times per second. Because compared to its 5V supply, the power earth, which is the world, now oscillates, because the device "doesn't know any better". So, then suddenly there's a lot of noise all around it.
So if there's a good enough power filter in the device (which there may not even be!) to filter any switching noise/ripple from the cheap supply and you make sure nothing's near it that relates to mains or power earth in any way (dangle it from a string in a hall with high ceilings?) you might be able to half the effect of the charger or even more. Of course, the cheap supply and its bad filtering and relatively high switching noise can still worsen the accuracy quite dramatically.
A fun experiment would be to turn the USB charger 180 degrees and see if that makes it better or worse, since then you flip the pin that has the phase on it, and might make the wobbling stop, if your neutral is well related to P.E. (Or it might make it start and give you 300 count of noise...)
Cheapest solution? Never measure with a USB charger attached.
Best 5V powered solution? High grade, very low noise 5V power supply, possibly with a built-yourself extra little common mode filter thingy, but preferably just with the negative supply pin connected to power earth. NOTING: If the supply is connected to power earth, so will the device be, which means it is no longer floating as a measurement device.
***Note: This practice of relating it a little sounds very stupid at first glance, but this is important in some/many switching designs to avoid dangerous effects in the transformer. In many designs the secondary and primary can differentially charge to kV's away from each other, which could break the safety barriers and cause much worse things than a tiny, tiny capacitor coupling could.