If I read the datasheet properly the accuracy specification on the FVR is +/- 3% so you're still within that window.
Vdd must be above 4.75V and there's a comment saying the specification is valid for the industrial temperature range part only. What's your Vdd and exact part number?
Also, are you doing any filtering/averaging in your code? You might benefit from that if you have noise coupled into your signal which your DMM filters out.
/Henrik.
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