Thanks to Jalbrekt...

[dustinspeer]

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...I spent all of my lunch break at 2 am trying to figure out a problem he messaged me. He asked me to post statistical breakdown of the scores using sectionalized AMCAS data. So here goes... By the way, if anything is incorrect that ya see, change it. It was 2 am. And I am not a math major.

mean:26.9
s.d.:6.6
Percentages equal the percent of people who got that score or less. Like for 26, we see that .44574% scored this or lower. This would be the percentile for a 27, the percent who scored lower than 27. The number in parentheses is the number of people who *probably* got that score based on the overall n. Enjoy!

45: .99693 (36886)
44: .99519 (36822.03)
43: .99262 (36726.94)
42: .98890 (36589.30)
41: .98365 (36395.05)
40: .97640 (36126.80)
39: .96601 (35286.16)
38: .95368 (35286.16)
37: .93701 (34668.37)
36: .91600 (33892.00)
35: .89011 (32934.07)
34: .85896 (31781.52)
33: .82230 (30425.10)
32: .78014 (28865.18)
31: .73275 (27111.75)
30: .68069 (25185.53)
29: .62480 (23117.60)
28: .56616 (20947.92)
27: .50602 (18722.74)
26: .44574 (16494.37)
25: .38670 (14307.90)
24: .33017 (12216.29)
23: .27727 (10258.99)
22: .22889 (8468.93)
21: .18565 (6869.05)
20: .14788 (5471.56)
19: .11564 (4278.68)
18: .08873 (3283.01)
17: .06678 (2470.86)
16: .04929 (1823.73)
15: .03567 (1319.79)
14: .02530 (936.10)
13: .01758 (650.46)
12: .01196 (442.52)
11: .00797 (294.89)
10: .00520 (192.40)
9: .00332 (122.84)
8: .00207 (76.59)
7: .00126 (46.62)
6: 7.481E-4 (27.68)
5: 4.301E-4 (15.91)
4: 2.376E-4 (8.79)
3: 1.237E-4 (4.58)
2: 5.780E-5 (2.14)
1: 2.057E-5 (.76)

 

[rxfudd]

I think I see what's not right here - assuming you calculated Z scores for normalized data, there should be symmetry about the score 26.9 - as it is, >36,000 people are scoring a 45 (clearly not true, unfortunately).

You have a cumulative graph going here - not a bell curve. The left hand values are correct (0.99693 for 45), but the right hand values don't reflect this. I'm not sure how you came up with these values (although I think I have an idea), so I will leave it to some other statistics buff to fix them.

By the way - you take your lunch break at 2am?? I thought I had a tough schedule...

 

[dustinspeer]

I'm sorry, in my slumber, I forgot to state that those were cumulative percentages, percentiles. So for 45, .99693 scored that or below. I know this seems impossible that .3% scored above a 45, but its just the way the normal curve is, you can't really change it for a stopping point of 45.

 

[dustinspeer]

And my shift at the hospital is 7p-7a, so I join the other graveyarders breaking at about 1 or 2 in the AM. Its a hard life but the pay is good. Ever hear of shift differentials? 🙂

 

[rxfudd]

Originally posted by dustinspeer:
•And my shift at the hospital is 7p-7a, so I join the other graveyarders breaking at about 1 or 2 in the AM. Its a hard life but the pay is good. Ever hear of shift differentials? 🙂•

Graveyard shift is the BEST!! When my lab goes to Brookhaven to do experiments, I'm always very popular around then because I'm willing to work the 8PM-8AM shifts. Something about working in the night that really works for me...

 

[dustinspeer]

Me too! I love it, but my wife HATES me being gone 3 nights a week. It only sucks when I go to class the next day. I keep a full time 15 hours while doing it. Gotta love the money!

 

[Jalby]

Damn. I feel so guilty now. I thaught it would be a 20 minute thing at most. That's what I get for never taking statistics. Thanks a lot for doing this for me. I hope other people enjoy it as much as I have. I love overanalyzing stuff. If we ever end up at the same interview I'll buy you breakfast, lunch, or dinner.

 

[audeo]

To the OP, how did you come up with the standard deviation? I am surmising that you just added standard deviations of individual sections coming up with such a high composite std. However, the std of the composite score should be root mean square of individual std. s^2 = s1^2 + s2^2 + s3^2. So if std of individual sections were all 2, the composite std should be 2root2 which is 2.828 instead of 6. As for average score, you just add three of them up.

 

[audeo]

Sorry it is 2root3 not 2root2. Therefore, it is around 3.4.