In more detail
The formula diastolic + (systolic − diastolic) / 3, equivalently (systolic + 2 × diastolic) / 3, weights diastolic pressure more because at resting heart rates the heart spends about two thirds of each cycle relaxing. At fast heart rates diastole shortens and the estimate becomes less accurate; monitors connected to an arterial line calculate the true mean from the pressure waveform. The difference between systolic and diastolic is the pulse pressure.
Why it matters
MAP reflects the pressure that pushes blood through the organs. A MAP of roughly 70 to 100 mmHg is usual, and in intensive care a MAP below about 65 mmHg is commonly treated as a sign that organs may be under-perfused. It does not replace systolic and diastolic readings for diagnosing high blood pressure, and readings should be interpreted by a clinician in context.
Example
120/80 mmHg: 80 + (120 − 80) / 3 = 93.3 mmHg (pulse pressure 40)
150/95 mmHg: 95 + (150 − 95) / 3 = 113.3 mmHg (pulse pressure 55)
90/50 mmHg: 50 + (90 − 50) / 3 = 63.3 mmHg (below 65)