What is the correct method to calculate the Z score for a variable between two groups

I have two groups 23 Patients and 27 controls with a list for there age and the head circumference measurements I want to do scatter plot for the Z score of age by the Z score of head circumference. I will simplify the matter by the following table for 4 controls and 5 patients:

GROUP age head circumference
Patient 5 20 cm
Patient 7 19 cm
Patient 4 22 cm
Patient 8 17 cm
Patient 6 18 cm
Control 9 17 cm
Control 3 23 cm
Control 4 21 cm
Control 6 24 cm
I want to do scatter plot for the Z score of age by the Z score of head circumference. My question is about the correct method in this case to calculate the Z score for age and head circumference between the groups (I will mention the possible ways that I am thinking about regarding how to calculate Z score for age for example)

1. Z score patients = { age - mean age (patients)}/STD(patients) and Z score controls = { age - mean age (controls)}/STD(controls)
2. Z score patients = { age - mean age (controls)}/STD(controls) and Z score controls = { age - mean age (patients)}/STD(patients)
3. Z score patients = { age - mean age (controls)}/STD(controls) and Z score controls = { age - mean age (controls)}/STD(controls)