Definition of AVERAGE?!?

[doc toothache]

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This thread can be summed up in three words... blah blah blah

Seriously who cares?

Actually one is more than enough.

 

[UIC]

What came into question was not your calculations, but rather the absurdity of your example with nice round number of scores ranging neatly from 18-22 and the 37,500 enrollees considering US ds enroll 4500/year.

Thats why I said if you TAKE OFF THE ADDITIONAL ZERO from my example so that you have 2,500 getting 18, 800 getting 19, 300 getting 20, 100 getting 21, and 50 getting 22, then you would have 3,750 enrollees........ which is a bit more realistic. Either way average would be still 18.4.

 

[UCB05]

Thats why I said if you TAKE OFF THE ADDITIONAL ZERO from my example so that you have 2,500 getting 18, 800 getting 19, 300 getting 20, 100 getting 21, and 50 getting 22, then you would have 3,750 enrollees........ which is a bit more realistic. Either way average would be still 18.4.

Your example just plain doesn't work. As doc has pointed out, this is absurd and just does not exist in the real world.
Even if your example is remotely possible (remember we're still talking OVERALL DAT scores, not applying, accepted, enrolled, on SDN), aside from the mistake of using 18 instead of 17, your calculations are off. Try 18.506 which rounds up to 19. Furthermore, the top 500 (98.7 percentile) who you gave a standardized score of 22 should have been about a 26. The 1000 in the 96 percentile should have been a 23-24, not a 21. So your final average would have been even higher, thereby leaving more below the average.
Aside from an absurdly distorted peaky curve about the mean with a very small left shift (the 18s-22s in your example), where almost everyone had the same raw score which then places them in the same percentiles about the mean, you just can't have a meaningful set of standard scores ranging 18-22 above the mean of 18 (or 17 for that matter) without an equal amount of weight below the mean. 17 is an arbitrary number assigned to the mean by the DAT to standardize the raw scores on a 30 scale. To claim that you can have a meaningful set of standard scores above the mean in the near absence of standard scores below the mean is ridiculous.

 

[UIC]

Your example just plain doesn't work. As doc has pointed out, this is absurd and just does not exist in the real world.
Even if your example is remotely possible (remember we're still talking OVERALL DAT scores, not applying, accepted, enrolled, on SDN), aside from the mistake of using 18 instead of 17, your calculations are off. Try 18.506 which rounds up to 19. Furthermore, the top 500 (98.7 percentile) who you gave a standardized score of 22 should have been about a 26. The 1000 in the 96 percentile should have been a 23-24, not a 21. So your final average would have been even higher, thereby leaving more below the average.
Aside from an absurdly distorted peaky curve about the mean with a very small left shift (the 18s-22s in your example), where almost everyone had the same raw score which then places them in the same percentiles about the mean, you just can't have a meaningful set of standard scores ranging 18-22 above the mean of 18 (or 17 for that matter) without an equal amount of weight below the mean. 17 is an arbitrary number assigned to the mean by the DAT to standardize the raw scores on a 30 scale. To claim that you can have a meaningful set of standard scores above the mean in the near absence of standard scores below the mean is ridiculous.

Ok its enough aruging with you. If someone else want to give him a try and try to explain to him the purpose of my hypothetical example in the first place. Go ahead.

 

[UCB05]

lol this guy just doesnt admit it when he is wrong...

UIC was giving a HYPOTHETICAL scenario in which supertank's statement WOULD BE WRONG. Is the scenario logical? YES. is it right? No (unless you're talking about enrolled stats and not overall stats). THAT IS WHY IT IS A HYPOTHETICAL scenario. The DIFFERENCE that you don't understand here is that Supertank used a number rounded to the nearest WHOLE number as his average, while UIC used a number rounded to the TENTHs place as his average, which makes a WORLD of a difference.

Supertank said that there should be more 16s than 20s if the average is 17. The OP gave a hypothetical scenario where this would be incorrect. if the average is 17.4, this does NOT have to mean there are more 16s than 20s, and he showed why in his example (albeit with a different set of numbers) . why r u so ticked off about this.


You focus too much on the numbers and don't seem to have the ability to think above and beyond what is explicitly stated. This seems to be a problem with students who do nothing but study and has lost all ability to survive in the real world. This is why the MCAT reading comprehension is such a great test and should be on the DAT instead of the joke RC we have at the moment.

1. UIC giving example scores of 18 19 20 21 and 22 does not mean its not possible to get a score of 1-17 or 23-30, it just means in his example, no one got these scores. It is tedious and unnecessary to say 0 people got a 1, 0 people got a 2... all the way to how many people got a 30. The number set is 1-30, not 18-22. The number set of 1-30 is IMPLIED. It is implied this his numbers are part of the DAT standardized scale, as that is what this thread is about.

2. Stating that someone got a 18 does not mean their raw score is an 18, it is implied the 18 is already the standardized score. if i go into a thread and said i got an 18, it is implied i got the already standardized score of 18 (for whatever section the thread was about)

3. Supertank said that if the average is a 17, then 16s are more prevalent than 20s. This is correct even with UICs example if you fail to realize how the DAT is graded, which you say you are an expert at. BUT since we are talking about DAT scores, we all know they are represented with a greater degree of certainty. So IF the average is given to the tenths or hundredths place, like the scores we usually see in charts and whatnot, then the HYPOTHETICAL example presented by UIC holds water. A HYPOTHETICAL average presented by ADA of 17.4 does not necessarily mean there are more 16s and below than 20s or whatever and above, as supertank stated, and UIC showed why.

If you simply said like doc tooth said that UIC's example doesn't exist in the real world, then that is fine. But you said the example in of itself is incorrect, which it is not, because he made the wrong conclusion, which he did not.

for someone who tries SOOO hard to sound smart, you are coming off as the total opposite. this is my last post and if through all this you still don't get it, it may be too much work to help u any longer.

So much air, so little sense. UIC's example was wrong for many reasons beside the absurdity of it occurring.

 

[UCB05]

Ok its enough aruging with you. If someone else want to give him a try and try to explain to him the purpose of my hypothetical example in the first place. Go ahead.

UIC,
No need for arguing and I apologize for coming across heavy. My objection to your example was that it just does not exist. Not just in the real world sense that doc pointed out, but in statistics world as well. On a set of standard scores w/ 30 point scale (like the DAT) that has 17 arbitrarily set at the average raw score, you simply can not have a set of standardized scores such as you used in your hypothetical example. A standard scale assigns a standard score (18, 19, 22, 25, 16) based on the deviation (that the corresponding raw score was) from the average raw score. Simply put, your 22s (500 of them) on a real standardized scale would have been 25-27 (98.7 percentile). I realize that your intention was to produce a tight set of numbers just barely above a very very common "lowest score" to show how the "average" was basically the same as the lowest score, yet still have scores above and none below the "average". You can do that with raw scores (ie: 55/100, 56/100, 57/100, 58/100, 59/100), but you can't with standard scores. By using standard scores with such a tight grouping about the lowest standard score (17 or 18), you violated/ignored the entire premise of what standard scores are all about.

For argument sake, we can use the set of raw scores above to finally clarify this discussion. 25,000 (55), 8000(56), 3000(57), 1000 (58), 500 (59) has an average of 55.51. On a standard scale of 30, there would be 25,000 16's, 8000 18's, 3000 21's, 1000 23's and 500 26's. Which only proves SuperTank's original point that there are more 16's than 20's and which is why I said "you're using a raw score example (out of 30 possible questions)" Again, my apologies.

 

[iBeast]

You're a fool if you believe every score you see posted here on SDN.