How PSLE Aggregate and T-Scores are calculated

Now that the dust has settled, we can perhaps take a look at the most asked, yet least answered question about the PSLE. That question is –

How are PSLE Aggregate Scores calculated?

To understand how PSLE Aggregate Scores are calculated, we must first understand T-Score. T-Score is the adjusted score a student will get for a subject, after a series of tabulations has been made.

Formula for T-Score


X = Raw score of student
Y = Average Score of the whole cohort
Z = Standard Deviation* (SD)

Standard Deviation* (SD) is the spread of the marks around the average.

Example 1 -
Allan, Bernard and Charles have $45, $50 and $55 respectively. They have an average of $50 each.

Example 2 -
Dan, Edward and Frank have $10, $50 and $90 respectively. They also have an average of $50 each.

In Example 1, the spread ($45 to average of $50 and $55 to average of $50) is smaller than the spread in Example 2, where the spread is bigger ($10 to average of $50 and $90 to average of $50)

As such, Example 1 will have a smaller SD, as compared to Example 2.

A more detailed explanation of how SD is calculated can be found in this link.


Simpler Way to read Standard Deviation (SD)

If the average score of 3000 pupils who sat for Science Test is 50 marks and the SD is 5, it means that 2/3 of the 3000 pupils have scored 5 marks around the average, which means 2000 of the students scored from 45 to 55 marks.

If the average score of the same 3000 pupils who sat for Mathematics Test is 50 marks and the SD is now 10, it means that 2/3 of the 3000 pupils have scored 10 marks around the average, which means 2000 students scored from 40 to 60 marks.


Example of how T-score is calculated

Li Ting’s score for Mathematics – 90 (X)
Average score of cohort – 75 (Y)
Standard Deviation - 20 (Z) (this means 2/3 of cohort scored from 55 to 95)

Using the T-Score formula

T = 50 + 10(X – Y) / Z

T = 50 + 10 x (90 – 75) / 20

= 50 + 10 x 15/20

= 50 + 10 x 0.75

= 57.5

Li Ting’s T-score for Mathematics is 57.5

Now that we have covered T-score, we can take a look at PSLE Aggregate Score.


Using T-Score to Calculate PSLE Aggregate Score

Let’s now take a look at Li Ting’s total performance



The cohort’s average and standard deviation plays a big part in Li Ting’s score. To demonstrate, let’s move the average scores of all subjects down by 10 marks each, keeping all other variables (raw score and SD) constant. This is how Li Ting’s score will now look like.




Take note that Li Ting’s aggregate goes up from 245 to 260 when the averages of all subjects went down by 10 marks each. This shows that if the cohort is weaker, Li Ting’s aggregate score will increase, even if she scores the same marks for all the subjects.

It is therefore not accurate to compare a student’s aggregate score in a particular year, to the aggregate score of another student in a different year. Each year will have a different average for all the subjects.

Parents who have more than 1 child, tend to compare each child’s PSLE Aggregate Score with his/her sibling's score. This is not a very fair comparison.


Final Note –

Because PSLE aggregate score is based on T-scores, theoretically, there is no such thing as “maximum aggregate score”.

Many parents believe the (non-existent) maximum aggregate is 300. That is a misconception.

To demonstrate, I have bumped up Li Ting’s score (in Table 3) to full marks for all her subjects, using the same averages and SDs found in Table 2.




Note that although Li Ting scored 100% marks for all subjects, her PSLE Aggregate Score is only 286. She did not score the (imaginary and non-existent maximum) PSLE Aggregate Score of 300!

The only way to score that 300 (or even above that), is to have a very weak cohort in your year.


So if our imaginary Li Ting scored 100% for all her subjects and still only scored 286 for her PSLE Aggregate, how did Ms Natasha score a PSLE Aggregate of 294 for the year 2007? I don’t have the stats, but my guess is that the averages and SDs of the individual subjects of the cohort played a big role.

In any case, 294 is a respectable score, and we should give credit where it is due. It is an all time high and Ms Natasha definitely deserves the recognition for her outstanding performance.

I hope the article in this post gives parents and students a better picture how PSLE Aggregate Scores are calculated.


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