Some interesting discussions about HbA1c and meter readings in some posts in this thread, but there is more to it.
If you use a CGM which takes a sample every 5 minutes, and then upload the data to the software, it will give you the mean and the SD over the period you choose. The same applies to a "spot" BG meter (although, as stated, some will also display on the meter the 7-day, 14-day, 30-day, and 90-day means, and the number of samples).
To sample a repetitive waveform (such as sinewave or fixed-ratio square-wave etc), you should sample at twice the frequency at fixed intervals. But if the waveform is quasi-random or random, then the sampling interval can also be random, but with a rate that should be double the rate from maximum to minimum. So if you have one large swing per day, you do not need to catch that large swing, you only need to sample at a higher rate than the largest swings.
To prove my point, from personal experience, for several years my HbA1c was between 6.5% and 7.1% (taken at typically 6-monthly intervals). But, on my meter, my average was 11 mmol/l with an SD of 5 !!!!
My specialist said that the HbA1c was the more reliable of the two, but the closer I questioned this, with more and more examples (at each consultation) of waveform sampling, the more I became convinced that the meter was telling the truth. As a result, a "blind" CGM was used on me for 6 days, which gave an average of 10.5 and an SD of 5 !!!
So why was the HbA1c so wildly wrong ?
The answer is that the HbA1c test is not always correct, it depends on many factors. Anemia is one factor (not the only one) that makes HbA1c read low, and BG read high. There is another test called Fruxtosamine, which I had, and guess what, it came out at an equivalent HbA1c of 9% (Fructosamine is not the same at all, and it only measures the average over 3 weeks, but there is a table for equivalence).
Thus, if there is a wide discrepancy between HbA1c and average BG on your meter, there is reason to doubt the HbA1c, providing that you are "sampling" frequently enough over the same 90-day period. Note that, typically, average BG should be about 1 (no more than 2) mmol/l higher than the percent of the hbA1c
e.g. average BG of 7.5 and HbA1c of 6% is fine, average BG of 9 and HbA1c of 6% is questionable (provided there is sufficient sampling on the meter, my typical sample-rate is 500 times in 90 days)