The average BG and HbA1c are not directly related. The HbA1c is directly related to the exposure that red blood cells have had to glucose. If you were to look at a line graph of time on the x-axis and BG on the y-axis, then the area under the line (called AUC, or Area Under the Curve in the pharma industry) is what is directly related to the HbA1c.
Average BG is only loosely related. Using the median would be a better measurement, it's what I do in my day job of measuring AUC for oncology drugs, but for some reason machines only calculate the mean. Spikes in BG will cause more damage to the AUC, but less damage to your average BG. Also, everyone has differences in the lifetime of their red blood cells, which affect HbA1c values too. My latest HbA1c was 6.1%, but my average BG was 6.4 mmol/l. Compare this to Robert who had a higher average, but a better HbA1c.
Also, the error in the HbA1c measurement is normally around +/- 0.2%.
The best thing is to reduce variability, a steady BG level in single figures will give you a good HbA1c, whereas one with high variability, but the same average will give a worse HbA1c.
Sorry for the essay!