lee_yl:VitoRelax:[quote=\"lee_yl\"]
It is unlikely that two T-score could be the same as the T-score for any subject is a function of the variance and mean of the cohort's raw scores in that subject. While the published T-score is rounded up, rumor has it that in MOE's database, the actual T-score is stored up to 13 decimal places. And it is based on this actual T-score that students are ranked for their school selection.
Even though it is unlikely but it is still possible.
if 2 students taking the same 4 subjects in PSLE and got the same raw marks for the 4 subjects, of course their pale T-score will be identical even if it is 1000 decimal places.
Both students, their papers taken are subjected to the same mean and variance. So of course their t-score will be identical. Eg, if say both take Maths and both got 70 raw marks. Both will be subjected to the same mean & variance for maths. So no matter how you bell curve it, this 2 students with raw marks of 70 after subjected to bell curve will get the same numbers for maths up to even 10,000 decimal places !
So, if they take same 4 subjects and got the same raw marks, their t-score will be identical up to even 100,000 decimal places !
What is the probability of at least 2 students scoring the same for every subject?
From a layman perspective, it may be easy to have the same raw score for subjects like Maths and Science but for languages, especially those involving subjective marking like composition and oral, the likelihood is smaller.
From a statistical perspective, assuming a Gaussian distribution (due to the large population and central limit theorem) and applying continuity correction to discrete variables, the probability of more than 2 students scoring the same in one subject ranges between 0.01 to 0.05. For the same 2 students to have the exact same score in 4 subjects, the probability could range from (0.01)^4 to (0.05)^4, assuming that these are independent variables. Not zero but very low probability.[/quote]OMG, now we are getting out of topic by discussing about Gaussian distribution with CLT to work out the probability of 2 students scoring the same marks. U sure you can use Gaussian distribution for this purpose ? Can I know what will you plot on the x-axis and what will you plot on the y-axis ? Also, what are the discrete variables that you are plotting ?
You said that
\"from a layman perspective, it may be easy to have the same raw score for subjects like Maths and Science but for languages, especially those involving subjective marking like composition and oral, the likelihood is smaller.\" But why would language be any different. Say, the full marks for composition is 20, do your children get marks like 15.12435 out of 20 ? Of course NOT. What they will get is something like 15.5 or 15.0 or 12.5 or 13.0, it's to nearest half mark ! Same for oral and whatnot !
So, from common sense and example provided by Augmum, we can see that it is not impossible. To apply Gaussian distribution to find the probability is like getting a rocket to go from Pasir Ris to Jurong ....
Perhaps, sometimes too much studying can make one gone bonkers and lost touch with reality ! But then again, sometimes, applying a theorem without actually understanding is even more dangerous.
Cheers
