HSC and ATAR (9 of 10) - Calculation of the ATAR

Aggregate
After the scaling process is complete, it is now possible to add the scaled marks together. To determine the aggregate, 10 units of ATAR courses are chosen comprising:
. the best 2 units of English
. the best 8 units from the remaining courses, which can include up to 2 units of Category B courses
Basing on Alex's scaled marks, his aggregate is calculated as follows:
                              Scaled                           Total
Course                     mark           Unit            mark
English Advanced      41.8             2               83.6
History Ext.               45.4             1               45.4
Maths Ext. 2             42.8              2              85.6
Economics                42.5              2               85.0
Maths Ext. 1             37.2              2               74.4
Modern History         24.9              1               24.9

Aggregate                                   10              398.9

ATAR Percentile
With the aggregate calculated, the ATAR percentile which shows the position of the student relative to his ATAR cohort (i.e. Year 12 students eligible for an ATAR) is determined. Following is a table of the ATAR percentile corresponding to some selected aggregate in 2012 (as shown in Report of the Scaling of the 2012 NSW HSC by BOS):
                        Aggregate                  ATAR Percentile
                           450.0                             98.8
                           400.0                             91.1
                           350.0                             77.0
                           300.0                             60.1
                           250.0                             42.9
                           200.0                             26.7
                           150.0                             13.7
As can be seen from the table, Alex's aggregate of 398.9 is close to the 91.1-percentile. His actual ATAR percentile may have been calculated as 90.9 (i.e. Alex's position in the HSC is higher than 90.9% of all other students).

Year 7 Percentile
Next, the Year 7 percentile which shows the position of the student relative to his Year 7 cohort is determined. This is done by incorporting the number of students who had started Year 7 study at the same time with the student but do not complete their study in Year 12. From the Australian Bureau of Statistics (ABS), a comparison can be made between the size of the Year 12 cohort in 2012 and that of the Year 7 cohort in 2007. Statistics shows that there are early school leavers of 6,739. As these 6,739 students virtually receive no marks in the HSC, it can be expected the Year 7 percentile would be higher than the corresponding ATAR percentile (i.e. the student's performance will be better than more other students including the early school leavers). Following is a table of the Year 7 percentils corresponding to the ATAR percentile in 2012 (as shown in Report of the Scaling of the 2012 NSW HSC by BOS):
                     ATAR Percentile       Year 7 Percentile
                            99.0                          99.4
                            90.0                          94.1
                            80.0                          88.2
                            70.0                          82.1
                            60.0                          76.0
                            50.0                          69.6
                            40.0                          62.8
                            30.0                          55.3
                            20.0                          46.5
                            15.0                          41.5
As can be seen from the table, Alex's ATAR percentile of 90.9 is close to 90.0 (corresponding to a Year 7 percentile of 94.1). His actual Yeat 7 percentile may have been calculated as 94.24 (i.e. Alex's position in the HSC is higherr than 94.24% of all other students starting Year 7 together with him).

The ATAR
The final step for calculating the ATAR is just to truncate the Year 7 percentile to the nearest 0.05. In so doing, Alex's ATAR is 94.25.