HbA1c, as you probably know, represents the average blood concentration over a long period of time. Depending on the individual's life-style practices, variations can be found. However, if the HbA1c is very high, it is more likely that their fasting blood glucose level will also be significantly higher than 110mg/dl.

Since you are using very vague terms like "not very high" and "very high" for the two parameters, perhaps this the best that can done. 

Sir, thanks for the answer. That's true what you are saying and I know that but I have seen, have many reports, that many people have there fasting glucose say 170 or 180 and their HbA1c is 9 or 10 while a few had FPG 310 with HbA1c almost 7. How can we define this discrepancy at a point of time when there blood sample was withdrawn?

As I already mentioned, and you already seem to know, a single fasting blood glucose level represents the situation of that specific moment on that day whereas HbA1c is the representation of the average blood glucose for a few months.

In the case of your example of FBG 310 and A1c ~7, you know that if even the average blood glucose was ~300mg/dl,much less the fasting, which should be lower than average, the A1c would be ~12. The only way these values are possible is through some other issues of which you were not aware, for example an infection (or something drastically changing about the status of patient's disease, such as loss of islet mass/function). Alternatively, the patient with abnormal GT could have not told you the whole story - after an overnight fast, felt hungry and on the way to your clinic couldn't resist sweets freshly being made!

Your first example is not too surprising, perhaps the person is in his or early phase of better management of diabetes and the lowered values are not yet reflected at the level of A1c. Alternatively, longer than normal fasting time. 

As integration to what said by Tausif, always use HbA1c as endpoint of metabolic control in your patients over about 8-weeks. That's the parameter you have to discuss with your patient to take under control: fasting glucose and pills/insulin are the tools to control HbA1c.

Thank you sir for your kind reply.

Hi, I got to know about this question now.

Here is a simple practical explanation to your query (as per my clinical experience). HbA1c level strongly correlates to FPG in an individual in standard condition (regular life without any external stimulus i.e. sudden uptake of sweet at an instant and/or any anti-diabetic medication) and this correlation is irrespective of diabetic or non-diabetic condition. At the same time HbA1c represents an average plasma glucose level over last 8-12 weeks.

Thus, in case of FPG=310 and HbA1c =7 means

1. The subject may be diabetic who was under control for last 8-12 weeks (low HbA1c) and has suddenly (2-7 days) the diabetes is out of control due to some factors (poor diet management/ drug resistant that need to be changed).  OR

2. The subject is not diabetic and has taken excess sugar/alcohol late at night.

That's satisfactory Nayak sir. Thank you sir for your kind reply.

I do not agree with the last Nayak's # 2 point.

310 FPG is by definition a diabetic state. It is also diabetes after an oral glucose load.

I agree with Luigi.  Any FBG that exceeds a defined limit is by definition a diabetic state.  310 exceeds any normal fasting level.  All the comments on the relationship between fasting glucose and A1c are correct.  Even those of us who are diabetics under control have deviations in blood glucose. The A1c as stated is an integrated value over 8-12 weeks.  Some one with variable high and low swings in blood glucose can have the same A1c as someone with tight control.  A1c gives you no measure of these swings and does not tell you if the patient has any hypoglycemic episodes.   If you are looking for some measure of control it would be important to try to find out if the patient has hypoglycemia. And how frequently? When you speak of correlations between the two measures you are looking at a number of observations on patients or subjects.  If you are looking at the general population without diabetics the maximum level for both the fasting glucose and the A1c are bounded by the maximum values of normal.  So the ranges are fairly tight and you would expect a higher degree of correlation.  If you look at diabetics only you have a much wider range for both measures so  your correlations are expected to be smaller.  On a general population sample of  subjects you would get variation and how much would depend on the prevalence of diabetes in you population.

American Diabetes Association publishes a chart of estimated average glucose which helps patients relate their A1c to the plasma glucose. 

http://www.diabetes.org/living-with-diabetes/treatment-and-care/blood-glucose-control/a1c/

The quick and dirty method in the clinic is to take A1c, subtract 2 and multiply by 30 to get estimated average glucose.

In regard to the patient question, A1c is a 3 month average. FPG of 310 in a patient who has an A1c of 7 may represent a developing loss of control or that they ate something that really torqued their sugar the night before or they have something like the Somogyi effect going on at night as George mentioned above.

A1c also is not useful in patients with hemorrhage, thalessemia and hemolytic anemias since it's based on red blood cells. 

Melissa makes an important point that I had forgotten about; with conditions affecting red blood cells the A1c is not accurate.  Often the need to address anemia and very low hematocrits is neglected.  Excellent point Melissa.

Some speculations: 

A1c high, FBG low:

1. high A1c- low FBG: past vs present, that might be effective treatment measures in the last days or weeks = A1c is still high but FBG already lower (e.g. initiation of pump treatment, intensification of oral treatment or else, delivery after pregnancy) - A1c represents the long term memory and even so, when metabolic state has changed 

2. falsely high A1c: as in state of renal insufficiency (carbamylation), acetacetylation, methylation, pathologically persistence of relatively old red cells. Analyse all clinical circumstances of the case.Try e.g. fructosamine determination for clarification. (Calculate the GlyQ  as fructosamine/A1c-relation)

A1c low, FBG high:

1. in T1-DM I would suppose a nightly low (SOMOGGHI effect?) or a too short acting insulin dosage at previous evening.

2.Quite typically in new diagnosed cases with acute onset of diabetes  this addressed relation(low A1c-high BG) is not surprising,- So might be when e.g. Steroid-therapy is initiated and coming from quite well controlled metabolic state deterioration happens over hours and days after steroid start.

3. falsely low A1c: is seen in a lot of Hb-variant persons - check further A1c-methods: and find e.g. additional peaks when applying HPLC in the chromatogram or apply tina quant (R), that is only reactive to the end terminal aminoacids of Hb- B-chain and therefore quite insensible against variants.

overall: any misbalance of A1c vs BG stimulates and postulates detective work, but can - in most cases - be clarified.

Thanks a lot Dr. Henrichs for a nice explanation.