STATISTICS (Average scores etc)

[Arne]

Some stats for IMO 2005

Beware, they might be somewhat inaccurate because of counting mistakes, but they should be relatively okay, and at least it gives you an idea!

Right...

QUESTION 1

Question 1 was a bit tougher than expected this year. The average score for this very nice question is 2.61/7.

Number of students scoring 7/7: 140
Number of students scoring 6/7: 5
Number of students scoring 5/7: 10
Number of students scoring 4/7: 5
Number of students scoring 3/7: 19
Number of students scoring 2/7: 65
Number of students scoring 1/7: 57
Number of students scoring 0/7: 205

QUESTION 2

This one was quite easy for a Q2 but again very nice. The average score for this question was 3.11/7.

Number of students scoring 7/7: 176
Number of students scoring 6/7: 2
Number of students scoring 5/7: 7
Number of students scoring 4/7: 12
Number of students scoring 3/7: 7
Number of students scoring 2/7: 12
Number of students scoring 1/7: 200
Number of students scoring 0/7: 96

QUESTION 3

Again, a very nice algebra question by Hojoo Lee. This is his sixth question which makes the paper in 5 years, impressive! This question is not that hard for a Q3 but a lot of people didn't get anywhere with it. The average score is 0.92/7.

Number of students scoring 7/7: 55
Number of students scoring 6/7: 9
Number of students scoring 5/7: 0
Number of students scoring 4/7: 0
Number of students scoring 3/7: 0
Number of students scoring 2/7: 3
Number of students scoring 1/7: 22
Number of students scoring 0/7: 417

QUESTION 4

Funny little question this one. I think this is the right level for a Q4 or Q1. Very nice, again.

Number of students scoring 7/7: 239
Number of students scoring 6/7: 7
Number of students scoring 5/7: 3
Number of students scoring 4/7: 0
Number of students scoring 3/7: 0
Number of students scoring 2/7: 30
Number of students scoring 1/7: 134
Number of students scoring 0/7: 87

QUESTION 5

Beautiful geometry question, somewhat easyish for a Q5 (compared to last year's Q5 for example). The average for this question is 2.18/7 which is certainly not low.

Number of students scoring 7/7: 124
Number of students scoring 6/7: 8
Number of students scoring 5/7: 6
Number of students scoring 4/7: 4
Number of students scoring 3/7: 15
Number of students scoring 2/7: 30
Number of students scoring 1/7: 35
Number of students scoring 0/7: 284

QUESTION 6

Strange. I am personally not very fond of this question. It is certainly not extremely hard for a Q6, with an average score of 1.35/7.

Number of students scoring 7/7: 56
Number of students scoring 6/7: 6
Number of students scoring 5/7: 2
Number of students scoring 4/7: 15
Number of students scoring 3/7: 12
Number of students scoring 2/7: 54
Number of students scoring 1/7: 39
Number of students scoring 0/7: 322

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

The average for the competition is 13.97/42. The paper seems easier than last year's paper to me so the bronze cut of 12/42 is surprisingly low, in my opinion. An obvious explanation for this is the fact that there are so many new countries participating (these countries score pretty low and bring the bronze cut down). The paper was definitely quite nice this year.

[Stijn]

According to the official report (stats by Luis Cruz Romo), this should be corrected to:

QUESTION 1

Average score 2.61/7.
Number of students scoring 7/7: 141
Number of students scoring 6/7: 5
Number of students scoring 5/7: 11
Number of students scoring 4/7: 5
Number of students scoring 3/7: 20
Number of students scoring 2/7: 65
Number of students scoring 1/7: 59
Number of students scoring 0/7: 207

QUESTION 2

Average score 3.05/7.
Number of students scoring 7/7: 175
Number of students scoring 6/7: 2
Number of students scoring 5/7: 7
Number of students scoring 4/7: 11
Number of students scoring 3/7: 7
Number of students scoring 2/7: 13
Number of students scoring 1/7: 202
Number of students scoring 0/7: 96

QUESTION 3

Average score 0.91/7.
Number of students scoring 7/7: 55
Number of students scoring 6/7: 9
Number of students scoring 5/7: 0
Number of students scoring 4/7: 0
Number of students scoring 3/7: 0
Number of students scoring 2/7: 3
Number of students scoring 1/7: 23
Number of students scoring 0/7: 423

QUESTION 4

Average score 3.78
Number of students scoring 7/7: 240
Number of students scoring 6/7: 8
Number of students scoring 5/7: 6
Number of students scoring 4/7: 4
Number of students scoring 3/7: 16
Number of students scoring 2/7: 30
Number of students scoring 1/7: 145
Number of students scoring 0/7: 88

QUESTION 5

Average score 2.16/7
Number of students scoring 7/7: 125
Number of students scoring 6/7: 8
Number of students scoring 5/7: 6
Number of students scoring 4/7: 4
Number of students scoring 3/7: 16
Number of students scoring 2/7: 30
Number of students scoring 1/7: 36
Number of students scoring 0/7: 288

QUESTION 6

Average score 1.34/7.
Number of students scoring 7/7: 56
Number of students scoring 6/7: 6
Number of students scoring 5/7: 2
Number of students scoring 4/7: 15
Number of students scoring 3/7: 13
Number of students scoring 2/7: 57
Number of students scoring 1/7: 39
Number of students scoring 0/7: 325

TOTAL SCORES

Average score: 13.88/44

(Score - Number of participants - cumultative sum - rank)
Gold:
42 - 16 - 16 - 1
41 - 2 - 18 - 17
40 - 1 - 19 - 19
39 - 1 -20 - 10
38 - 2 - 22 - 21
37 - 6 - 28 - 23
36 - 6 - 34 - 29
35 - 8 - 42 - 35
Silver:
34 - 3 - 45 - 43
33 - 1 - 46 - 46
32 - 6 - 52 - 47
31 - 4 - 56 - 53
30 - 8 - 64 - 57
28 - 7 - 71 - 65
27 - 4 - 92 - 89
26 - 7 - 99 - 93
25 - 8 - 107 - 100
24 - 6 - 113 - 108
23 - 8 - 121 - 114
Bronze:
22 - 9 - 130 - 122
21 - 8 - 138 - 131
20 - 5 - 143 - 139
19 - 12 - 155 - 144
18 - 19 - 174 - 156
17 - 16 - 190 - 175
16 - 16 - 206 - 191
15 - 19 - 225 - 207
14 - 13 - 238 - 226
13 - 5 - 243 - 239
12 - 6 - 249 - 244
No medal:
11 - 12 - 261 - 250
10 - 17 - 278 - 262
9 - 19 - 297 - 279
8 - 25 - 322 - 298
7 - 6 - 328 - 323
6 - 13 - 341 - 329
5 - 15 - 356 - 342
4 - 12 - 368 - 357
3 - 27 - 395 - 369
2 - 49 - 444 - 396
1 - 41 - 485 - 445
0 - 28 - 513 - 486

[Valentin Vornicu]

Arne was pretty close