Post by: perpetual on July 19, 2013, 07:32:40 pm
Thanks.
Post by: vox nihili on July 19, 2013, 08:56:47 pm
I know that a 40 is top 9%, 45 is top 2% for the subjects with a high intake, but I need to find out the exact 'top %' of my 47 and 48 study scores from last year. Does anyone know how to calculate that?
Thanks.
http://stattrek.com/online-calculator/normal.aspx
Normal random variable (x)= [enter your score]
Cumulative probability: P(X < 40)= [enter nothing...this'll be your result!]
Mean= [see below]
Standard Deviation= [see below]
For the value of the mean and standard deviation, access the VCE scaling report: http://www.vtac.edu.au/pdf/scaling_report.pdf These values are in the second and third columns respectively.
Note: you can only do these for raw scores
Also note: the website may start off by saying "Normal Random Variable (z)". It will change to x once you've entered different values for mean and standard deviation.
Post by: vox nihili on July 19, 2013, 09:02:03 pm
I had to do a bit of back working from below, since just using a normal distribution with mean=30 and standard deviation=7 didn't give the below.
http://www.vcaa.vic.edu.au/pages/faqs/vcecurrentstudents.aspx
The following seems to work, if you want to know, then find
using a normal distribution with mean=30 and standard deviation=7.
Since you don't have methods in your sig, try this link http://www.wolframalpha.com/input/?i=Pr%28X%3E45-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
BUT replace the 45 with your scores, and remember this is only an approximate figure.
So for 47 and 48 we have top 0.92% and 0.62%.
http://www.wolframalpha.com/input/?i=Pr%28X%3E47-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
http://www.wolframalpha.com/input/?i=Pr%28X%3E48-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
Just so that everyone else doesn't go off at me and say that it's not right, here is the calculation to each example given from the VCAA website using this method. It seems to work since you can only get a discrete study score, and not halfway between integers.
http://www.wolframalpha.com/input/?i=Pr%28X%3E45-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
http://www.wolframalpha.com/input/?i=Pr%28X%3E40-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
http://www.wolframalpha.com/input/?i=Pr%28X%3E35-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
http://www.wolframalpha.com/input/?i=Pr%28X%3E30-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
http://www.wolframalpha.com/input/?i=Pr%28X%3E25-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
http://www.wolframalpha.com/input/?i=Pr%28X%3E20-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
In reality, the standard deviation and the mean never end up being exactly 7 and 30 respectively. Makes it a bit confusing when they specifically say what you've quoted. They underestimate who is actually interested in that rubbish! hahah
Post by: b^3 on July 19, 2013, 09:04:35 pm
Post by: lala1911 on July 19, 2013, 09:33:32 pm
Post by: vox nihili on July 19, 2013, 09:44:51 pm
Yeah I know, I forgot that we get the individual means and standard deviations for each subject... I've been out of this for a while :P
I got half way through it and thought, shit...this is all wrong! I don't think that calculating study scores is the pinnacle of mathematical knowledge though, so we're safe! haha
Post by: Professor Polonsky on July 19, 2013, 10:42:44 pm
bcub3d's (previously deleted, now reposted below) post, and the post Lala linked to, are as accurately as we can predict the distributions.
Post by: b^3 on July 19, 2013, 10:52:13 pm
I'll just put the post back here then.
I had to do a bit of back working from below, since just using a normal distribution with mean=30 and standard deviation=7 didn't give the below.
http://www.vcaa.vic.edu.au/pages/faqs/vcecurrentstudents.aspx
The following seems to work, if you want to know
Since you don't have methods in your sig, try this link http://www.wolframalpha.com/input/?i=Pr%28X%3E45-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
BUT replace the 45 with your scores, and remember this is only an approximate figure.
So for 47 and 48 we have top 0.92% and 0.62%.
http://www.wolframalpha.com/input/?i=Pr%28X%3E47-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
http://www.wolframalpha.com/input/?i=Pr%28X%3E48-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
Just so that everyone else doesn't go off at me and say that it's not right, here is the calculation to each example given from the VCAA website using this method. It seems to work since you can only get a discrete study score, and not halfway between integers.
http://www.wolframalpha.com/input/?i=Pr%28X%3E45-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
http://www.wolframalpha.com/input/?i=Pr%28X%3E40-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
http://www.wolframalpha.com/input/?i=Pr%28X%3E35-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
http://www.wolframalpha.com/input/?i=Pr%28X%3E30-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
http://www.wolframalpha.com/input/?i=Pr%28X%3E25-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
http://www.wolframalpha.com/input/?i=Pr%28X%3E20-0.5%29%2C+normal+distribution%2C+mean%3D30%2C+sd%3D7
Post by: vox nihili on July 19, 2013, 10:59:06 pm
Gotta love those moments. "Ohhh no, you've got to take this exception" *feel really smart*..."you actually don't need to at all"...."oh"
And this I daresay is exactly why you're doing Eng and I'm not! haha ;)
Post by: Lasercookie on July 19, 2013, 11:05:34 pm
Post by: b^3 on July 19, 2013, 11:07:46 pm
So more or less, t-rav's method will be for scaled study scores in a specific year, whilst b^3's method would be for raw study scores? The difference between the two being whether you're taking the mean of 30 and std. dev of 7, or the ones from the VTAC scaling report (though taking the intervals of .5 as b^3 stated?)I think t-rav's method would work given the scaled score, I wonder how close the two values would be.