This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

Friday, November 23, 2007

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.

=============

Anonymous said...

Thanks for this highly informative website. With your experience, I hope you would answer my following questions:

(1) Are the PSLE subjects graded according to one's raw scores or graded after the marks have been moderated. Example, if one scored 88 marks for Science in a tough paper, would it be an A or A*?

(2) If one consistently scored 75% for English based on top schools' standard, will it translate to an average, below average, or above average performance in the PSLE?

Thanks!

Excel Eduservice said...

Hello,

1) All scores will go through the T-score calculation. As to the details on the manner how they are marked, MOE has been very silent and "secretive" about that. Even many teachers and principals themselves are in the dark and do not know the whole picture. You can try calling MOE up, but I seriously doubt it will be worth your while.

2) Personally, I feel that as far as English is concerned, the papers from "top schools" and "other schools" vary not as much as the Maths or Science papers. As such, I would prefer to be conservative. Hence, if a student scores about 70 to 75 for top school papers, that should be about what he or she would score for PSLE.

Anonymous said...

I am not able to find out under what circumstances a student can fail PSLE.
How are students taking PSLE assessed to be 'not ready for secondary schools' ?

Anonymous said...

is it true that the passing mark for PSLE 20?

Excel Eduservice said...

To anonymous,

Believe in yourself. You can make it!

Anonymous said...

It is preety good to read your article posted today..Thanks for the detailed T Score information..Since this year my son is taking PSLE exam, i am trying to understand how the PSLE score works..It is pity that many of the PSLE students who are sitting in the exam are now aware and understand fully of the T-Score including many of the parents.. Having gone thru your explanation, i am verymuch understand about this T-Score. I shall pass this website information to other parents who are taking PSLE exam.

Thanks

Anonymous said...

i made a small spelling mistake..in my previous posting, i had mentioned

"It is pity that many of the PSLE students who are sitting in the exam are now aware" shoud be read as not aware

Anonymous said...

hai

Anonymous said...

Hello,

I was just wondering, what happens if the marks a student gets for a subject is lower than the average of the whole cohort? Will the student get zero for that subject even if he had a B for that subject? Wouldn't that be unfair, Like, getting 185 for the grades A A B A.
Thanks

Excel Eduservice said...

If someone scores below average of the whole cohort, the aggregate score will be less than 200.

200 is the average of every year's cohort.

Anonymous said...

This is so fake.The PSLE score is not calculated like that!

Anonymous said...

PSLE T-score is calculated like that. Is it true that the average is 200 of each year?

Excel Eduservice said...

Statistically, the average should be 200. That’s because the t-score will force the average of each subject to be 50.

Using the forumula

T = 50 + 10 x (Raw Score – Mean)/SD

So if the raw score of the pupil = average (mean) of the cohort,

T = 50 + 10 x (0)/SD

T = 50 + 0

T = 50

That is average for 1 subject.

If the student scores the exact average of the cohort for all subjects ----

4 subjects x 50 = 200.

So it should be 200 as average.

Anonymous said...

Hi, So does it mean that for this year highest is 287 which is 7 points lower than in 2007. The overall COP for most schools will be lower as well ?

Excel Eduservice said...

Q:Hi, So does it mean that for this year highest is 287 which is 7 points lower than in 2007. The overall COP for most schools will be lower as well ?

A: No, it does not work that way.

Anonymous said...

in tat case do u think choosing a sec sch 2-3 points this year is much riskier.

Anonymous said...

sorry i mean 2-3 points above my score as 1st choice. i got 241 but i chosen bt panjang which is 243.

Anonymous said...

How does the different number of pupils taking the various MT affect the calculation of individual subject T-score? In other words, is there an advantage to top score in a MT with a much smaller number of pupils taking the same MT?

Excel Eduservice said...

Q: How does the different number of pupils taking the various MT affect the calculation of individual subject T-score? In other words, is there an advantage to top score in a MT with a much smaller number of pupils taking the same MT?

A: I really have no idea. There are so many "smaller number" of MTs like French, Tamil, Urdu etc. I have no idea how well they have done. Maybe you can try asking some senior teachers in your school.

Anonymous said...

Wow....

Anonymous said...

Hi I have this burning doubt for past so many months. Please clarify. Is the average for each mother tongue calculated individually? I mean a different average each for chinese, malay, tamil etc., What happens to srudents who have taken non-tamil india languages under BTTSAL? My son has taken hindi and i'm worried that his score will be lower on average compared with other MT. Some one please let me know where i can clarify this doubt.

Thanks
Anu

Excel Eduservice said...

Anu, it is best you check out with MOE itself.

Anonymous said...

Hi, is it true that 'importance' of English and Chinese is "double" that of Maths and Science since it is total 200 marks for English and also Chinese? Or may I ask what is the 'ideal' total T-score for each subject to arrive at total of 300? I was told to put a lot more emphasis on English and Chinese since it is 200 marks for each of these 2 subjects. Thank you!

Excel Eduservice said...

Grace,

There is no bias towards any subject. Everything is even.

Here is a more detailed explanation.

Anonymous said...

My PSLE got 3 As and 1 A* but my aggregrate is only 199 I got A in Math,MT and Science and A* in english while my sister got 2 As and 2 Bs.She got As in English and maths and B in MT and science and got 239.Me and my sister are twins please explain.

Excel Eduservice said...

I have never come across any student with 3As, 1A* and yet, a score of 199. Can’t explain. Did you try to appeal?

Your sister’s score looks more typical of a 2A, 2B student.

Anonymous said...

I am very worried about my daughter she got all As and scored 228 and she got posted to Loyang Sec please explain it to me.I am very grateful

Excel Eduservice said...

The Aggregate score is based on the score of the student against the cohort. The grades (A*, A, B etc) are the student’s personal grades, without considering the performance of the cohort.

A particular student may score 1A* and 3As, which may hover near the 90% mark for the 3As and 90+ or even 100 for the A*. That may give him or her 260+ for an aggregate score.

Another student may score 4As, but he or she have scored just above the B grade. That may give around 230 as the aggregate score.

Since only the grades and aggregate score and not the individual scores are shown, students and parents may think that there is a disparity, since it appears that 1A* can give a variance of about nearly 30+ points in aggregate.

To be able to calculate the aggregate score, you must know the individual subjects’ scores as well as the cohort’s averages and standard deviations.

Anonymous said...

I almost repeated P6 I am in EM3 my aggregate was 99 Is it possible to fail everything and go to express like with grades like EDEE

Anonymous said...

Is it true that PSLE is slightly easier than what pupils normally think? Because I bought the PSLE booklet and the questions are quite easy.

I scored : 248

248 from my school's SA1

Anonymous said...

did you take your score over 400 times 0.7? Or did you times 0.75? If you times 0.7, then your score is superb!

Anonymous said...

Hm...I times 0.72

345 x 0.72 = 248.4

Anonymous said...

Good post. High T-scores are impacted by
(A) A high raw score
(B) A low average (mean)
(C) A low Standard deviation

I feel (C) namely the Standard deviation plays the most important part of these 3. Could you plz tell me from you 'gut feel' or estimate:
(1) What is the level of SD?
(2) Is the SD high (20+) or low(below 15) for mother tongue?
Thanks!

Here are my estimation of average and SD to calculate T score base on some data I gathered from the web. Basically we know that for Math, national passing rate is 83% and those over 75 point is 42%. So mapping this to Student T Distribution, I can estimate the Average to be 60 point while the standard deviation (SD) to be 13. Please advise on my estimation.

Anonymous said...

The average T-score may or may not be 200 as the formula accounts for lower raw than mean score. i.e.
T=50+10((RS-MS)/SD)
...
T=50+10((-X)/SD)
T=50+(-10X)/SD
...
Will Result in:
T<50

Anonymous said...

Is it possible to score 3 A* and 1 A and get aggregate score of only 254?

Anonymous said...

yep, that means the A* are very low and A is also very low.

Anonymous said...

Thanks. Does A* means >= 91 & A >= 75 hold for PSLE scores? If not, what does A* imply?

Anonymous said...

HI,
i am more interested how was 2009 PSLE result for foundation maths. How do we calculate mean score & SD. I have daughter who will be sitting for 2010 PSLE with 3S & 1FMA

Anonymous said...

Hi, my child is very weak in all her subjects due to a medical condition. I'm considering dropping MT for PSLE so that she could focus on the other 3 subjects. Will taking only 3 subjects affect her overall T scores? Or is she better off taking foundation MT and still failing it? She's P5 this year. Thks!

Unknown said...

Hi i would like to know whether the same standard deviation is used for all subjects for a particular year?

ExcelEduservice said...

No. The std dev depends on the cohort's actual performance.

Anonymous said...

Anonymous said...

wish that we could get better result after reading this!

Anonymous said...

if this is the way PSLE results are calculated, i ought to hate my corhort. 2A* and 2As, yet my score is only 242.

Whilce said...

hello , i am exempted from MT. Do yo know how to calculate the aggregate score of 3 subjects ? please help

ExcelEduservice said...

Whilce, sorry I don't know how to calculate without MT. You have to ask your teacher.

Jian Rong said...

2010 PSLE:
If I get 86 for English, 99 for Maths, 91 for Chinese and 90 for Science, how much T-score would that be (just a range)?

ExcelEduservice said...

You have not included your oral and written comprehension marks.

However, assuming those scores are percentages of your subjects, you should be able to score 260+ to be on the conservative side.

Transformice Fans said...

Hi.

Very informative. Thanks

Anonymous said...

Hi, a very informative website indeed. I was just wondering what would be a rough estimated t-score for 98 in maths, 95 in english, 95 in mother tongue and 89 in science.

ExcelEduservice said...

To be on the conservative side, it would be above 265. Should qualify for top schools.

Please note that you have not factored Oral, Listening Comprehension and Paper 1 for the Languages. That will definitely affect your Aggregate Score as well.

Anonymous said...

Hi. thanks. What would be the t-score if the english and mother tongue scores were both 190. Thank you and please help.

ExcelEduservice said...

190 is a very high score for EL and MT. I have never had any student scoring that. I can't estimate.

Anonymous said...

Please try to provide me with a rough estimate.

:)

ExcelEduservice said...

If you can get 190 for both languages, it would mean you have scored 95% for EL and MT. If your Maths is 98 and Sc 89, to be on the conservative side, you can score above 270. 280 is possible, 290 is stretching it.

With such a high score, a lot depends on how your cohort does, because you are so far away from the mean. That is how T-score works.

The further you are away from the mean, the more your Aggregate score depends on your cohort's performance, which means the less predictable your Aggregate score will be.

Anonymous said...

Hi, can you tell me what are your estimations for the standard deviation and averages of the four subjects. Please give a rough estimation. Thank you!

ExcelEduservice said...

I have stopped teaching in schools for quite a few years. It would be better if you were to ask your teacher that.

Anonymous said...

hi,
how can it be possible for a student who scores 3B 1A getting aggregates of 217 which is higher than another student who scores 3A 1B with an agrregate of just 209? enlighten please! thanks in advance

Anonymous said...

Hi,

I would like to know if you get 102 for english,102 for chinese,80 for maths and 80 for science, will you still get to express class and pass? Please reply. Thanks.

ExcelEduservice said...

Different schools have different cut off points. You have to check with the schools for that.

Anonymous said...

hi, u have yet to reply my query wif regards to the 3B 1A (217) & 3A 1B (209) question..can u enlighten me pls..dis is a real situation..thks!!

ExcelEduservice said...

I do not know how that is mathematically possible, using the T-Score method of calculation. Maybe you can ask your teacher.

Anonymous said...

My son scored 3As & 1A*(MT)and an aggregate of 247. How would that translate to raw score?

ExcelEduservice said...

There is no way to accurately calculate the raw score by looking at the result slip.

Anonymous said...

Thank you SO much! i m taking PSLE this year n didnt figure out how the scores were calculated. thx a lot!

Anonymous said...

hello!
but i have a question,
1) what is the minimum score for express?
once again, thank you very much.

ExcelEduservice said...

It depends on the vacancies of the schools you apply. You can check it out at MOE's website to see past years' cut off for the different schools.

Anonymous said...

Hi, my son is taking PSLE this year. He has been getting 75 for MT, 60-65 Science, 48 -52 Maths and Eng 60-64. I also understand the school is setting difficult papers for them.Will it be easier in PSLE? I would like to know what would be the aggregate for 1A and 3Bs and 1A 2Bs and 1C and 2As and 2Bs

ExcelEduservice said...

It is difficult to predict the Aggregate Score with such a wide band. However, the average student scores from higher sixties to lower seventies. If a student scores that range, it would give about an aggregate score of 200.

Anonymous said...

Wow! The information is great! I am very grateful that I found this link!

However, I have a question:

Does Higher Mother Tongue affects one's aggregate? If yes, how does it affect? Please reply because I'm in a great dilemma now, ASAP. Thank you.

ExcelEduservice said...

Higher MT does not affect.

Anonymous said...

hi i m so impressed with your website taking PSLE this year and can you help me calculate the score for 91 83 75 95 ? THANKS

Anonymous said...

Higher MT will only be effective for certain schools isn't it ?

Anonymous said...

hi,
I am a PR with my kid taking PSLE next year. but my collegues says that next year is dragon kids taking PSLE so the competetion is very tough. is it true? how was the scores in past dragon years? My son normally gets A/A* in sceince/maths/english but week in MT (B). what can I expect the score to be? I know it differs from year to year but with too many children taking next year where does he stand?

Anonymous said...

Hi, I'm taking the PSLE this year, could you help me calculate the score for 88(Maths) 90.5(science) 185(English) and 185.5(Chinese)? Many thanks :)

Littleducky

Anonymous said...

TO Anonymous: september 8 2011
i don't believe you are a parent as u do not know how to spell weak

Anonymous said...

Hii I am taking PSLE this year..may I know what I should score for each subject if I want to score 260 and above?

Anonymous said...

Hi can you help me calculate my score for 189 (CL), 184 (EL), 90.5 (SC) and 88 (MA)? many thanks.

Anonymous said...

@anonymous september 11 2011:

I posted a comment on 8 september 2011 but apparently I didn't include the word weak in my post. Just to let you know.

Anonymous said...

Hi, my daughter is very weak in ALL her subjects. She got in her prelim: - Eng (C), MT (B), Math (E) and Sci (D)

How would her stand/ T-Score in the PSLE result? Any changes in passing and move forward to Sec1??

Thanks

Anonymous said...

My son will be taking his PSLE next year (dragon year cohort) am wondering what kind of aggregate score will he be getting should his percentage be as the followings
English- low 80s
Chinese - high 70s
Science - mid 80s
Math - mid 90s
Many thanks!

Anonymous said...

I would like to know how is PSLE T-score calculated for 3 subjects without MT as exemption have been allowed?

Anonymous said...

Hi!pls tell me more about PSLE passing marks n how to calculate without MT.Thankyou!

Anonymous said...

This isnt the correct info i was looking for.FAKE

Anonymous said...

Hi,my son scored C for all 4 subjects but only many aggregate of 147 N(T) but his friend got C for 3 subjects and E for 1 but has higher aggregate of 153 - is it possible? Also, with 4C - why so low score of 147 - possible? Tks

Anonymous said...

NO!!!!Almost 1 mark,just wanna know if you can go to secondary school if u get below COP!

Anonymous said...

.....I got my straight As can i ask if one can receieve the raw scores in each subject and the range of A and A*?

Anonymous said...

I have 1B, 2As and an A* for Maths. How is it possible to obtain such a low mark of 222?!

Anonymous said...

i think your A* is 1 mark above A,and your A are at most 5 marks above your B.Your B can be at most 3 marks above C.

Anonymous said...

Who score the lowest here?I score above 200

Anonymous said...

Hi, I got 3a* and 1a (sc) . But only got 257. Is it possible? I'm very confidence with my maths( can be a very high a*). Please advise! Thanks

Anonymous said...

SO good!257!!!!!!How do you do it?Do you study 7-8 hours everyday?

Anonymous said...

Do you know there are how many boys and girls who taken psle this year?
1) how many boys?
2) how many girls?

Anonymous said...

Thanks for revealing the T-score of the PSLE formula. I would just like to ask. Is there any stats on the recent averages of cohort and SD?
And if you get a raw score of 87 and your raw score is 92, does it mean that you get A*?
Thanks

๑ נεssιcα ๑ said...

Can you please tell me my T-Score and Aggregrate score etc. if I get 95 for Eng Math n Sci but 60 in CL and if I get 90 for Eng Math Sci but 70 or 75 in Cl. At least tell me a simple way to calculate cos I dun geddit.
-A P6 Girl who knows little of PSLE

ExcelEduservice said...

Without the SD and Mean, you can't calculate. But some parents do a very rough way by multiplying 3/4 (ie x 3/4) with the total of the four subjects.

Example if you get 95 for Eng, Maths, Sc but 60 for CL, then:

(90 + 90 + 90 + 60) x (3/4)

Anonymous said...

How much will I score if I get
Eng-74
Math-93
Chi-89
Sci-87
(prelim score)

ExcelEduservice said...

I am unable to calculate because we need to know the Std Dev which you do not have.

Roughly, if you want to be conservative, 245 should be no problem.

If you want to be more hopeful, 255 should be within your reach.

Anonymous said...

Hi there! Can you help me calculate my score according to these marks?

English : 94
Maths:89
Science: 89
Malay: 94

Average of cohort:
EL: 70
MA: 65
SC: 70
ML:66

SD:
EL: 55-75
MA: 45-65
SC: 60-70
ML: 54-66

ExcelEduservice said...

SD should be only one figure, not a range of figures. I have adjusted your SD based on your figures to 10, 10, 5, 6 for EL, MA, SC, ML respectively.

Here is what the workout looks like on the my electronic worksheet.

language, x, y, z, tscore
el, 94, 70, 10, 74
ma, 89, 65, 10, 74
sc, 89, 70, 5, 88
ml, 94, 66, 6, 96

Agg score 332

No one has scored this high. I suspect either your SD given is not accurate or you may be in a generally weak class.

Were you transferred from another school to be in such a clase?

Anonymous said...

Hello, I would appreciate it if you could advise me on the following:
1. Are A*, A etc. grades based on raw scores or moderated across the cohort's performance for that subject?
2. What would an estimated aggregate score be for this year's PSLE where science was the hardest paper, followed by maths(English and Chinese were about the same)with these scores:
English: 90
Chinese: 85
Maths: 98
Science: 90

ExcelEduservice said...

1. I have never marked PSLE papers and I am not privy to exactly how they moderate.

2. To calculate Agg score, you need mean and SD. But if you do not have them, one crude way is to add all your scores and multiply it by 3/4.

Jin Yuan said...

If you are interested to know how PSLE T score is computed for those students exempted from MT, according to Min(Edn), a pupil exempted from mother tongue is assessed based on his performance in English, Mathematics and Science. The total score of these three subjects is statistically adjusted so that it reflects an aggregate score comparable to those of his peers who offer mother tongue and have similar total scores for these three subjects.

http://sprs.parl.gov.sg/search/topic.jsp?currentTopicID=00078238-WA&currentPubID=00078241-WA&topicKey=00078241-WA.00078238-WA_1%23hansardContent43a675dd-5000-42da-9fd5-40978d79310f%23

IS said...

How is the score calculated for people who have approved exemption of PSLE(student who joined mid-year can appeal for exemption)? Is there any loss of score or something? Urgent, thank you.

Anonymous said...

How is the score for students who have been exempted from mother tongue calculated? Please reply ASAP

ExcelEduservice said...

I do not have the details of the answers you want. It would be best if you got it from MOE itself.

Anonymous said...

I am a parent who is the child of twins taking PSLE this year (snake cohort).I was wondering, if the twins like to stick with each other and they one gets low marks and the other extremely high, would it be better if I let the higher one go to the worse school or I put them in seperate schools? My elder is very smart and got 4A*s last year as said on her report book and my younger got 3D,1C.

ExcelEduservice said...

It is better for you to discuss the matter with your daughters’ teachers. They should know the situation better.

Anonymous said...

Hi.Thanks for all your suggestions. You wrote for mother tongue & English they will directly consider the marks out of 200.But in the book is mentioned for MT & English they have different weightage for each section. For example Oral is 25%, Compo is 27.5 % , LC is 10% and Paper 2 is 47.5% etc..So how they can calcluate directly for 200 marks and put T-score.?

Anonymous said...

Hi. My child graduated back in 2009. She scored 3A* for eng, Maths, and mt but B for science, and got 253.The science paper was considered quite easy that year. Anyone knows how much higher she can get if she scored A or A* for science(just a rough gauge or range)?