HbA1c is a measure of "average over a period of time". Mathematically an average is a pretty poor representation of a distribution of glucose levels. You will get the same average for the numbers 39, 40, 41 and the numbers 0,40 80. So what is the average telling you?
So the answer to you question is an average tells you nothing about your variance from the norm. There are 3 ways to lower an average.
1. Cut out the high spikes (eat less spikey foods or target exercise to remove them)
2. Lower all the measures (drugs, diet)
3. Skew your distribution towards the lower numbers (exercise, drugs)
Hope that answers your question!