What diagnostic test measures average blood glucose levels over time for diabetes?

The correct choice is the test that measures the average blood glucose levels over time for diabetes, which is glycosylated hemoglobin, commonly known as HbA1c. This test provides crucial information about a patient's average blood glucose levels over the past two to three months. It reflects the percentage of hemoglobin that has glucose attached to it, thus giving a longer-term perspective on glucose management compared to individual blood glucose tests.

In clinical practice, monitoring HbA1c is essential for evaluating how well a diabetes management plan is working. It helps healthcare providers assess whether a patient is maintaining their blood sugar levels within the recommended range, thereby reducing the risk of complications associated with diabetes.

The other options serve different purposes: fasting blood tests measure blood glucose levels after a period of fasting, providing a snapshot rather than a trend over time. Random blood glucose tests assess glucose levels at any time of the day but also offer a momentary measure. A chest X-ray is unrelated to glucose measurements and is typically used to evaluate respiratory or cardiovascular conditions. Thus, the glycosylated hemoglobin test is the only option that specifically analyzes and indicates long-term glucose control, making it the definitive choice for the question.